(* Content-type: application/vnd.wolfram.cdf.text *) (*** Wolfram CDF File ***) (* http://www.wolfram.com/cdf *) (* CreatedBy='Mathematica 9.0' *) (*************************************************************************) (* *) (* The Mathematica License under which this file was created prohibits *) (* restricting third parties in receipt of this file from republishing *) (* or redistributing it by any means, including but not limited to *) (* rights management or terms of use, without the express consent of *) (* Wolfram Research, Inc. 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Para ello necesitamos que f est\[EAcute] definida en \ puntos arbitrariamente pr\[OAcute]ximos a ", Cell[BoxData[ FormBox[ RowBox[{"(", RowBox[{ SubscriptBox["x", "0"], ",", SubscriptBox["y", "0"]}], ")"}], TraditionalForm]]], ", es decir que haya puntos del ", Cell[BoxData[ FormBox[ RowBox[{"Dom", " ", "f"}], TraditionalForm]]], " a cualquier distancia de ", Cell[BoxData[ FormBox[ RowBox[{"(", RowBox[{ SubscriptBox["x", "0"], ",", SubscriptBox["y", "0"]}], ")"}], TraditionalForm]]], ". No descartamos la posibilidad de el dominio de ", Cell[BoxData[ FormBox["f", TraditionalForm]]], " incluya ", Cell[BoxData[ FormBox[ RowBox[{"(", RowBox[{ SubscriptBox["x", "0"], ",", SubscriptBox["y", "0"]}], ")"}], TraditionalForm]]], ". Para que se cumplan estos objetivos ", Cell[BoxData[ FormBox[ RowBox[{"(", RowBox[{ SubscriptBox["x", "0"], ",", SubscriptBox["y", "0"]}], ")"}], TraditionalForm]]], " debe ser un punto de acumulaci\[OAcute]n. " }], "Text", FontSize->18], Cell[TextData[{ "Podemos definir l\[IAcute]mite como sigue:\nSea f: D \[Subset] \ \[DoubleStruckCapitalR]\[RightArrow]", Cell[BoxData[ FormBox[ SuperscriptBox["\[DoubleStruckCapitalR]", "2"], TraditionalForm]]], " y sea ", Cell[BoxData[ FormBox[ RowBox[{"(", RowBox[{ SubscriptBox["x", "0"], ",", SubscriptBox["y", "0"]}], ")"}], TraditionalForm]]], " un punto de acumulaci\[OAcute]n de D y sea un ", Cell[BoxData[ FormBox["l", TraditionalForm]]], " \[Element] \[DoubleStruckCapitalR]. Se dice que ", Cell[BoxData[ UnderscriptBox["lim", RowBox[{ RowBox[{"(", RowBox[{"x", ",", "y"}], ")"}], "\[Rule]", RowBox[{"(", RowBox[{ SubscriptBox["x", "0"], ",", SubscriptBox["y", "0"]}], ")"}]}]]], FontSize->18], " ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"f", "(", RowBox[{"x", ",", "y"}], " ", ")"}], "=", " ", "l"}], TraditionalForm]]], ", si ", Cell[BoxData[ FormBox[ RowBox[{"\[ForAll]", RowBox[{"\[Epsilon]", ">", "0", " "}]}], TraditionalForm]]], Cell[BoxData[ FormBox[ RowBox[{"\[Exists]", RowBox[{"\[Delta]", ">", "0", " "}]}], TraditionalForm]]], " tal que ", Cell[BoxData[ FormBox[ RowBox[{"(", RowBox[{"x", ",", "y"}], ")"}], TraditionalForm]]], "\[Element]D,", Cell[BoxData[ FormBox[ RowBox[{"|", RowBox[{ RowBox[{"f", "(", RowBox[{"x", ",", "y"}], ")"}], " ", "-", "l"}], "|", RowBox[{"<", "\[Epsilon]", " "}]}], TraditionalForm]]], " siempre que ", Cell[BoxData[ FormBox[ RowBox[{"0", "<", SqrtBox[ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"x", "-", SubscriptBox["x", "0"]}], ")"}], "2"], "+", SuperscriptBox[ RowBox[{"(", RowBox[{"y", "-", SubscriptBox["y", "0"]}], ")"}], "2"]}]], "<", "\[Delta]"}], TraditionalForm]]] }], "Text", FontSize->18], Cell[TextData[{ "Ejercicio.- Generalicese la definici\[OAcute]n de limite a ", Cell[BoxData[ FormBox["n", TraditionalForm]]], " varibles en ", Cell[BoxData[ FormBox[ SuperscriptBox["\[DoubleStruckCapitalR]", "n"], TraditionalForm]]], ". 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Para calcular los l\[IAcute]mites seg\[UAcute]n la direcci\[OAcute]n de \ aproximaci\[OAcute]n a ", Cell[BoxData[ FormBox[ RowBox[{"(", RowBox[{ SubscriptBox["x", "0"], ",", SubscriptBox["y", "0"]}], ")"}], TraditionalForm]]], " podemos utilizar la siguiente proposici\[OAcute]n.\nSi existe ", Cell[BoxData[ FormBox[ RowBox[{"\[Epsilon]", ">", "0", " "}], TraditionalForm]]], "tal que todos los puntos de ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"B", "(", RowBox[{"a", ",", "\[Epsilon]"}], ")"}], " "}], TraditionalForm]]], ", con ", Cell[BoxData[ FormBox["a", TraditionalForm]]], " = ", Cell[BoxData[ FormBox[ RowBox[{"(", RowBox[{ SubscriptBox["x", "0"], ",", SubscriptBox["y", "0"]}], ")"}], TraditionalForm]]], ", pertenecientes a D [Observaci\[OAcute]n: ", Cell[BoxData[ FormBox[ RowBox[{"(", RowBox[{ SubscriptBox["x", "0"], ",", SubscriptBox["y", "0"]}], ")"}], TraditionalForm]]], " puede no pertenecer a D] y ", Cell[BoxData[ FormBox[ RowBox[{"l", "=", RowBox[{ UnderscriptBox["lim", 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m\[AAcute]ximo" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"A", "/.", RowBox[{"{", RowBox[{"\[Lambda]", "->", RowBox[{"-", FractionBox["5", "2"]}]}], "}"}], " ", RowBox[{"(*", "Maximo", "*)"}]}]], "Input"], Cell[BoxData[ RowBox[{"-", "5"}]], "Output"] }, Open ]], Cell["El m\[AAcute]ximo est\[AAcute] en", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"z", "[", RowBox[{ RowBox[{"-", FractionBox["4", "5"]}], ",", " ", RowBox[{"-", FractionBox["3", "5"]}]}], "]"}]], "Input"], Cell[BoxData["11"], "Output"] }, Open ]], Cell[TextData[{ "Para \[Lambda] = ", Cell[BoxData[ FractionBox["5", "2"]]], " \[CapitalDelta] >0 , y A>0, luego hay un m\[IAcute]nimo" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"A", "/.", RowBox[{"{", RowBox[{"\[Lambda]", "->", FractionBox["5", "2"]}], "}"}], RowBox[{"(*", "M\[IAcute]nimo", "*)"}]}]], "Input"], Cell[BoxData["5"], "Output"] }, Open ]], Cell["El m\[AAcute]ximo est\[AAcute] en", "Text"], Cell[CellGroupData[{ Cell[BoxData[ 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Method->{"RotationControl" -> "Globe"}, PlotRange->{{0, 5}, {0, 3}, {-314.9999500714305, 3.3673469256546547`}}, PlotRangePadding->{ Scaled[0.02], Scaled[0.02], Scaled[0.02]}], TraditionalForm]], "Output"] }, Open ]], Cell["\<\ Buscamos primero los puntos estacionarios del interior de S. \ \>", "Text", FontSize->16], Cell[BoxData[{ RowBox[{ FractionBox[ RowBox[{ RowBox[{"\[PartialD]", "f"}], RowBox[{"(", RowBox[{"x", ",", "y"}], ")"}], " "}], RowBox[{ RowBox[{"\[PartialD]", "x"}], " "}]], "=", " ", RowBox[{ RowBox[{"9", " ", "-", " ", RowBox[{"12", RowBox[{"(", RowBox[{"x", "+", "y"}], ")"}]}]}], "=", RowBox[{ RowBox[{"0", " ", "\[Rule]", " ", RowBox[{"12", RowBox[{"(", RowBox[{"x", "+", "y"}], ")"}]}]}], "=", " ", "9"}]}]}], "\n", RowBox[{ FractionBox[ RowBox[{ RowBox[{"\[PartialD]", "f"}], RowBox[{"(", RowBox[{"x", ",", "y"}], ")"}], " "}], RowBox[{ RowBox[{"\[PartialD]", "y"}], " "}]], "=", " ", RowBox[{ RowBox[{"8", " ", "-", " ", RowBox[{"12", RowBox[{"(", RowBox[{"x", "+", "y"}], 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RowBox[{"0", " ", StyleBox["e", FontWeight->"Plain", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"CompatibilityType"->0, "Masked"->False, "Outline"->False, "RotationAngle"->0, "Shadow"->False, "StrikeThrough"->False, "Underline"->False}], " ", "x"}], " ", "\[Element]", RowBox[{"(", RowBox[{"0", ",", "5"}], ")"}]}]}]}], TraditionalForm]]], " \[Rule] ", Cell[BoxData[ FormBox[ RowBox[{" ", RowBox[{ RowBox[{"f", "(", RowBox[{"x", ",", "0"}], ")"}], "=", RowBox[{ RowBox[{"9", " ", "x"}], " ", "-", " ", RowBox[{"6", SuperscriptBox["x", "2"]}]}]}]}], TraditionalForm]]], "\[Rule]", Cell[BoxData[ FormBox[ RowBox[{" ", RowBox[{ RowBox[{ RowBox[{"f", "'"}], RowBox[{"(", RowBox[{"x", ",", "0"}], ")"}]}], "=", RowBox[{ RowBox[{"9", " ", "-", " ", RowBox[{"12", "x"}]}], " ", "=", " ", "0"}]}]}], TraditionalForm]]], "\[Rule]Hay un m\[AAcute]ximo en ", Cell[BoxData[ FormBox["x", TraditionalForm]]], " = 3/4\[Rule]", Cell[BoxData[ FormBox[ RowBox[{"f", "(", RowBox[{ RowBox[{"3", "/", "4"}], ",", "0"}], ")"}], TraditionalForm]]], " = 27/8\n \n II) ", Cell[BoxData[ FormBox[ RowBox[{" ", RowBox[{"x", " ", "=", " ", RowBox[{ RowBox[{"5", " ", StyleBox["e", FontWeight->"Plain", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"CompatibilityType"->0, "Masked"->False, "Outline"->False, "RotationAngle"->0, "Shadow"->False, "StrikeThrough"->False, "Underline"->False}], " ", "y"}], " ", "\[Element]", RowBox[{"(", RowBox[{"0", ",", "3"}], ")"}]}]}]}], TraditionalForm]]], " \[Rule] ", Cell[BoxData[ FormBox[ RowBox[{" ", RowBox[{ RowBox[{"f", "(", RowBox[{"5", ",", "y"}], ")"}], "=", RowBox[{ RowBox[{"45", " ", "x"}], " ", "+", RowBox[{"8", " ", "y"}], " ", "-", " ", RowBox[{"6", SuperscriptBox[ RowBox[{"(", RowBox[{"5", "+", "y"}], ")"}], "2"]}]}]}]}], TraditionalForm]]], "\[Rule]", Cell[BoxData[ FormBox[ RowBox[{" ", RowBox[{ RowBox[{ RowBox[{"f", "'"}], RowBox[{"(", RowBox[{"5", ",", "y"}], ")"}]}], "=", RowBox[{ RowBox[{"8", " ", "-", " ", RowBox[{"12", 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.786 r F P 0 g s .49606 .67533 m .51692 .72147 L .47886 .7438 L p .696 .614 .761 r F P 0 g s .47886 .7438 m .45787 .69795 L .49606 .67533 L p .696 .614 .761 r F P 0 g s .49599 .68463 m .51692 .72147 L .47886 .7438 L p .713 .656 .792 r F P 0 g s .47886 .7438 m .4577 .70727 L .49599 .68463 L p .713 .656 .792 r F P 0 g s .39843 .67964 m .41988 .72307 L .38199 .75073 L p .721 .633 .76 r F P 0 g s .38199 .75073 m .36035 .70755 L .39843 .67964 L p .721 .633 .76 r F P 0 g s .4366 .65424 m .45787 .69795 L .41988 .72307 L p .711 .629 .764 r F P 0 g s .41988 .72307 m .39843 .67964 L .4366 .65424 L p .711 .629 .764 r F P 0 g s .39776 .69829 m .4196 .73243 L .38161 .76014 L p .741 .678 .789 r F P 0 g s .38161 .76014 m .35948 .72632 L .39776 .69829 L p .741 .678 .789 r F P 0 g s .53454 .6552 m .55528 .70164 L .51692 .72147 L p .685 .609 .765 r F P 0 g s .51692 .72147 m .49606 .67533 L .53454 .6552 L p .685 .609 .765 r F P 0 g s .53456 .66448 m .55528 .70164 L .51692 .72147 L p .7 .651 .798 r F P 0 g s .51692 .72147 m .49599 .68463 L .53456 .66448 L p .7 .651 .798 r F P 0 g s .43613 .67281 m .4577 .70727 L .4196 .73243 L p .73 .674 .796 r F P 0 g s .4196 .73243 m .39776 .69829 L .43613 .67281 L p .73 .674 .796 r F P 0 g s .47494 .63133 m .49606 .67533 L .45787 .69795 L p .7 .625 .769 r F P 0 g s .45787 .69795 m .4366 .65424 L .47494 .63133 L p .7 .625 .769 r F P 0 g s .3766 .63831 m .39843 .67964 L .36035 .70755 L p .726 .645 .768 r F P 0 g s .36035 .70755 m .33831 .66651 L .3766 .63831 L p .726 .645 .768 r F P 0 g s .57338 .63753 m .59402 .6843 L .55528 .70164 L p .673 .603 .769 r F P 0 g s .55528 .70164 m .53454 .6552 L .57338 .63753 L p .673 .603 .769 r F P 0 g s .57351 .64681 m .59402 .6843 L .55528 .70164 L p .687 .646 .803 r F P 0 g s .55528 .70164 m .53456 .66448 L .57351 .64681 L p .687 .646 .803 r F P 0 g s .47468 .64985 m .49599 .68463 L .4577 .70727 L p .718 .67 .802 r F P 0 g s .4577 .70727 m .43613 .67281 L .47468 .64985 L p .718 .67 .802 r F P 0 g s .41497 .61262 m .4366 .65424 L .39843 .67964 L p .716 .641 .772 r F P 0 g s .39843 .67964 m .3766 .63831 L .41497 .61262 L p .716 .641 .772 r F P 0 g s .51356 .61088 m .53454 .6552 L .49606 .67533 L p .689 .62 .773 r F P 0 g s .49606 .67533 m .47494 .63133 L .51356 .61088 L p .689 .62 .773 r F P 0 g s .45351 .5894 m .47494 .63133 L .4366 .65424 L p .705 .636 .777 r F P 0 g s .4366 .65424 m .41497 .61262 L .45351 .5894 L p .705 .636 .777 r F P 0 g s .5135 .62937 m .53456 .66448 L .49599 .68463 L p .705 .666 .809 r F P 0 g s .49599 .68463 m .47468 .64985 L .5135 .62937 L p .705 .666 .809 r F P 0 g s .37541 .66623 m .39776 .69829 L .35948 .72632 L p .748 .693 .799 r F P 0 g s .35948 .72632 m .33681 .6946 L .37541 .66623 L p .748 .693 .799 r F P 0 g s .6127 .62232 m .63325 .66946 L .59402 .6843 L p .661 .597 .773 r F P 0 g s .61293 .63162 m .63325 .66946 L .59402 .6843 L p .672 .639 .809 r F P 0 g s .59402 .6843 m .57338 .63753 L .6127 .62232 L p .661 .597 .773 r F P 0 g s .59402 .6843 m .57351 .64681 L .61293 .63162 L p .672 .639 .809 r F P 0 g s .55254 .59287 m .57338 .63753 L .53454 .6552 L p .677 .614 .778 r F P 0 g s .53454 .6552 m .51356 .61088 L .55254 .59287 L p .677 .614 .778 r F P 0 g s .35435 .59904 m .3766 .63831 L .33831 .66651 L p .732 .657 .776 r F P 0 g s .33831 .66651 m .31581 .62753 L .35435 .59904 L p .732 .657 .776 r F P 0 g s .41409 .64041 m .43613 .67281 L .39776 .69829 L p .736 .69 .806 r F P 0 g s .39776 .69829 m .37541 .66623 L .41409 .64041 L p .736 .69 .806 r F P 0 g s .4923 .56862 m .51356 .61088 L .47494 .63133 L p .693 .631 .782 r F P 0 g s .47494 .63133 m .45351 .5894 L .4923 .56862 L p .693 .631 .782 r F P 0 g s .39295 .57303 m .41497 .61262 L .3766 .63831 L p .721 .653 .781 r F P 0 g s .3766 .63831 m .35435 .59904 L .39295 .57303 L p .721 .653 .781 r F P 0 g s .55269 .61136 m .57351 .64681 L .53456 .66448 L p .691 .66 .815 r F P 0 g s .53456 .66448 m .5135 .62937 L .55269 .61136 L p .691 .66 .815 r F P 0 g s .45293 .61711 m .47468 .64985 L .43613 .67281 L p .724 .686 .813 r F P 0 g s .43613 .67281 m .41409 .64041 L .45293 .61711 L p .724 .686 .813 r F P 0 g s .4317 .54949 m .45351 .5894 L .41497 .61262 L p .71 .649 .786 r F P 0 g s .41497 .61262 m .39295 .57303 L .4317 .54949 L p .71 .649 .786 r F P 0 g s .59197 .5773 m .6127 .62232 L .57338 .63753 L p .664 .608 .782 r F P 0 g s .57338 .63753 m .55254 .59287 L .59197 .5773 L p .664 .608 .782 r F P 0 g s .65258 .60959 m .67305 .65711 L .63325 .66946 L p .648 .59 .777 r F P 0 g s .63325 .66946 m .6127 .62232 L .65258 .60959 L p .648 .59 .777 r F P 0 g s .65293 .61892 m .67305 .65711 L .63325 .66946 L p .656 .633 .814 r F P 0 g s .63325 .66946 m .61293 .63162 L .65293 .61892 L p .656 .633 .814 r F P 0 g s .53144 .55027 m .55254 .59287 L .51356 .61088 L p .681 .626 .787 r F P 0 g s .51356 .61088 m .4923 .56862 L .53144 .55027 L p .681 .626 .787 r F P 0 g s .49203 .59628 m .5135 .62937 L .47468 .64985 L p .71 .681 .82 r F P 0 g s .47468 .64985 m .45293 .61711 L .49203 .59628 L p .71 .681 .82 r F P 0 g s .33159 .56177 m .35435 .59904 L .31581 .62753 L p .738 .67 .784 r F P 0 g s .31581 .62753 m .29277 .59059 L .33159 .56177 L p .738 .67 .784 r F P 0 g s .59234 .59582 m .61293 .63162 L .57351 .64681 L p .676 .654 .821 r F P 0 g s .57351 .64681 m .55269 .61136 L .59234 .59582 L p .676 .654 .821 r F P 0 g s .35249 .63623 m .37541 .66623 L .33681 .6946 L p .754 .709 .809 r F P 0 g s .33681 .6946 m .31354 .66495 L .35249 .63623 L p .754 .709 .809 r F P 0 g s .4707 .52837 m .4923 .56862 L .45351 .5894 L p .698 .644 .792 r F P 0 g s .45351 .5894 m .4317 .54949 L .4707 .52837 L p .698 .644 .792 r F P 0 g s .37046 .53544 m .39295 .57303 L .35435 .59904 L p .727 .666 .79 r F P 0 g s .35435 .59904 m .33159 .56177 L .37046 .53544 L p .727 .666 .79 r F P 0 g s .39151 .61005 m .41409 .64041 L .37541 .66623 L p .743 .706 .817 r F P 0 g s .37541 .66623 m .35249 .63623 L .39151 .61005 L p .743 .706 .817 r F P 0 g s .63196 .56419 m .65258 .60959 L .6127 .62232 L p .65 .601 .786 r F P 0 g s .6127 .62232 m .59197 .5773 L .63196 .56419 L p .65 .601 .786 r F P 0 g s .57102 .53433 m .59197 .5773 L .55254 .59287 L p .667 .619 .792 r F P 0 g s .55254 .59287 m .53144 .55027 L .57102 .53433 L p .667 .619 .792 r F P 0 g s .53149 .57792 m .55269 .61136 L .5135 .62937 L p .695 .676 .827 r F P 0 g s .5135 .62937 m .49203 .59628 L .53149 .57792 L p .695 .676 .827 r F P 0 g s .69314 .59936 m .71354 .64729 L .67305 .65711 L p .634 .583 .78 r F P 0 g s .67305 .65711 m .65258 .60959 L .69314 .59936 L p .634 .583 .78 r F P 0 g s .6936 .60872 m .71354 .64729 L .67305 .65711 L p .64 .625 .819 r F P 0 g s .67305 .65711 m .65293 .61892 L .6936 .60872 L p .64 .625 .819 r F P 0 g s .40947 .51155 m .4317 .54949 L .39295 .57303 L p .715 .662 .796 r F P 0 g s .39295 .57303 m .37046 .53544 L .40947 .51155 L p .715 .662 .796 r F P 0 g s .51003 .50966 m .53144 .55027 L .4923 .56862 L p .685 .638 .797 r F P 0 g s .4923 .56862 m .4707 .52837 L .51003 .50966 L p .685 .638 .797 r F P 0 g s .43068 .58638 m .45293 .61711 L .41409 .64041 L p .73 .703 .825 r F P 0 g s .41409 .64041 m .39151 .61005 L .43068 .58638 L p .73 .703 .825 r F P 0 g s .63255 .58276 m .65293 .61892 L .61293 .63162 L p .659 .647 .827 r F P 0 g s .61293 .63162 m .59234 .59582 L .63255 .58276 L p .659 .647 .827 r F P 0 g s .30828 .52648 m .33159 .56177 L .29277 .59059 L p .744 .684 .793 r F P 0 g s .29277 .59059 m .26914 .55564 L .30828 .52648 L p .744 .684 .793 r F P 0 g s .4487 .49008 m .4707 .52837 L .4317 .54949 L p .703 .657 .802 r F P 0 g s .4317 .54949 m .40947 .51155 L .4487 .49008 L p .703 .657 .802 r F P 0 g s .5714 .56203 m .59234 .59582 L .55269 .61136 L p .679 .67 .834 r F P 0 g s .55269 .61136 m .53149 .57792 L .5714 .56203 L p .679 .67 .834 r F P 0 g s .4701 .5652 m .49203 .59628 L .45293 .61711 L p .716 .699 .833 r F P 0 g s .45293 .61711 m .43068 .58638 L .4701 .5652 L p .716 .699 .833 r F P 0 g s .61116 .52083 m .63196 .56419 L .59197 .5773 L p .653 .613 .796 r F P 0 g s .59197 .5773 m .57102 .53433 L .61116 .52083 L p .653 .613 .796 r F P 0 g s .67262 .55354 m .69314 .59936 L .65258 .60959 L p .636 .594 .79 r F P 0 g s .65258 .60959 m .63196 .56419 L .67262 .55354 L p .636 .594 .79 r F P 0 g s .5498 .49336 m .57102 .53433 L .53144 .55027 L p .671 .632 .802 r F P 0 g s .53144 .55027 m .51003 .50966 L .5498 .49336 L p .671 .632 .802 r F P 0 g s .34745 .4998 m .37046 .53544 L .33159 .56177 L p .733 .68 .799 r F P 0 g s .33159 .56177 m .30828 .52648 L .34745 .4998 L p .733 .68 .799 r F P 0 g s .32894 .60828 m .35249 .63623 L .31354 .66495 L p .761 .726 .82 r F P 0 g s .31354 .66495 m .28959 .63739 L .32894 .60828 L p .761 .726 .82 r F P 0 g s .73448 .59165 m .75483 .64003 L .71354 .64729 L p .619 .576 .783 r F P 0 g s .71354 .64729 m .69314 .59936 L .73448 .59165 L p .619 .576 .783 r F P 0 g s .73506 .60107 m .75483 .64003 L .71354 .64729 L p .622 .616 .824 r F P 0 g s .71354 .64729 m .6936 .60872 L .73506 .60107 L p .622 .616 .824 r F P 0 g s .67344 .57219 m .6936 .60872 L .65293 .61892 L p .641 .639 .833 r F P 0 g s .65293 .61892 m .63255 .58276 L .67344 .57219 L p .641 .639 .833 r F P 0 g s .36833 .58172 m .39151 .61005 L .35249 .63623 L p .749 .724 .828 r F P 0 g s .35249 .63623 m .32894 .60828 L .36833 .58172 L p .749 .724 .828 r F P 0 g s .48826 .47101 m .51003 .50966 L .4707 .52837 L p .689 .652 .808 r F P 0 g s .4707 .52837 m .4487 .49008 L .48826 .47101 L p .689 .652 .808 r F P 0 g s .50987 .54648 m .53149 .57792 L .49203 .59628 L p .7 .694 .841 r F P 0 g s .49203 .59628 m .4701 .5652 L .50987 .54648 L p .7 .694 .841 r F P 0 g s .38673 .47555 m .40947 .51155 L .37046 .53544 L p .721 .676 .806 r F P 0 g s .37046 .53544 m .34745 .4998 L .38673 .47555 L p .721 .676 .806 r F P 0 g s .61187 .5486 m .63255 .58276 L .59234 .59582 L p .662 .663 .841 r F P 0 g s .59234 .59582 m .5714 .56203 L .61187 .5486 L p .662 .663 .841 r F P 0 g s .40787 .55768 m .43068 .58638 L .39151 .61005 L p .736 .721 .837 r F P 0 g s .39151 .61005 m .36833 .58172 L .40787 .55768 L p .736 .721 .837 r F P 0 g s .65194 .50977 m .67262 .55354 L .63196 .56419 L p .638 .605 .801 r F P 0 g s .63196 .56419 m .61116 .52083 L .65194 .50977 L p .638 .605 .801 r F P 0 g s .5901 .47946 m .61116 .52083 L .57102 .53433 L p .656 .625 .807 r F P 0 g s .57102 .53433 m .5498 .49336 L .5901 .47946 L p .656 .625 .807 r F P 0 g s .42624 .45371 m .4487 .49008 L .40947 .51155 L p .708 .672 .813 r F P 0 g s .40947 .51155 m .38673 .47555 L .42624 .45371 L p .708 .672 .813 r F P 0 g s .71405 .54539 m .73448 .59165 L .69314 .59936 L p .62 .586 .794 r F P 0 g s .69314 .59936 m .67262 .55354 L .71405 .54539 L p .62 .586 .794 r F P 0 g s .28433 .49314 m .30828 .52648 L .26914 .55564 L p .75 .698 .802 r F P 0 g s .26914 .55564 m .24484 .52267 L .28433 .49314 L p .75 .698 .802 r F P 0 g s .52824 .45432 m .5498 .49336 L .51003 .50966 L p .674 .646 .814 r F P 0 g s .51003 .50966 m .48826 .47101 L .52824 .45432 L p .674 .646 .814 r F P 0 g s .55007 .53022 m .5714 .56203 L .53149 .57792 L p .683 .688 .848 r F P 0 g s .53149 .57792 m .50987 .54648 L .55007 .53022 L p .683 .688 .848 r F P 0 g s .44764 .53612 m .4701 .5652 L .43068 .58638 L p .721 .717 .846 r F P 0 g s .43068 .58638 m .40787 .55768 L .44764 .53612 L p .721 .717 .846 r F P 0 g s .32383 .46608 m .34745 .4998 L .30828 .52648 L p .739 .695 .809 r F P 0 g s .30828 .52648 m .28433 .49314 L .32383 .46608 L p .739 .695 .809 r F P 0 g s .7151 .56416 m .73506 .60107 L .6936 .60872 L p .622 .631 .838 r F P 0 g s .6936 .60872 m .67344 .57219 L .7151 .56416 L p .622 .631 .838 r F P 0 g s .77672 .58651 m .79703 .63537 L .75483 .64003 L p .604 .568 .786 r F P 0 g s .75483 .64003 m .73448 .59165 L .77672 .58651 L p .604 .568 .786 r F P 0 g s .77743 .59601 m .79703 .63537 L .75483 .64003 L p .603 .607 .828 r F P 0 g s .75483 .64003 m .73506 .60107 L .77743 .59601 L p .603 .607 .828 r F P 0 g s .46605 .43426 m .48826 .47101 L .4487 .49008 L p .694 .667 .819 r F P 0 g s .4487 .49008 m .42624 .45371 L .46605 .43426 L p .694 .667 .819 r F P 0 g s .653 .53767 m .67344 .57219 L .63255 .58276 L p .643 .655 .847 r F P 0 g s .63255 .58276 m .61187 .5486 L .653 .53767 L p .643 .655 .847 r F P 0 g s .30466 .58239 m .32894 .60828 L .28959 .63739 L p .769 .744 .831 r F P 0 g s .28959 .63739 m .26488 .61192 L .30466 .58239 L p .769 .744 .831 r F P 0 g s .36344 .44146 m .38673 .47555 L .34745 .4998 L p .727 .692 .817 r F P 0 g s .34745 .4998 m .32383 .46608 L .36344 .44146 L p .727 .692 .817 r F P 0 g s .63105 .468 m .65194 .50977 L .61116 .52083 L p .64 .618 .812 r F P 0 g s .61116 .52083 m .5901 .47946 L .63105 .468 L p .64 .618 .812 r F P 0 g s .69349 .50119 m .71405 .54539 L .67262 .55354 L p .621 .597 .805 r F P 0 g s .67262 .55354 m .65194 .50977 L .69349 .50119 L p .621 .597 .805 r F P 0 g s .48774 .51702 m .50987 .54648 L .4701 .5652 L p .705 .712 .854 r F P 0 g s .4701 .5652 m .44764 .53612 L .48774 .51702 L p .705 .712 .854 r F P 0 g s .34448 .55543 m .36833 .58172 L .32894 .60828 L p .756 .743 .84 r F P 0 g s .32894 .60828 m .30466 .58239 L .34448 .55543 L p .756 .743 .84 r F P 0 g s .56875 .44004 m .5901 .47946 L .5498 .49336 L p .659 .639 .819 r F P 0 g s .5498 .49336 m .52824 .45432 L .56875 .44004 L p .659 .639 .819 r F P 0 g s .59083 .51643 m .61187 .5486 L .5714 .56203 L p .664 .681 .855 r F P 0 g s .5714 .56203 m .55007 .53022 L .59083 .51643 L p .664 .681 .855 r F P 0 g s .75637 .53979 m .77672 .58651 L .73448 .59165 L p .604 .578 .797 r F P 0 g s .73448 .59165 m .71405 .54539 L .75637 .53979 L p .604 .578 .797 r F P 0 g s .40325 .41923 m .42624 .45371 L .38673 .47555 L p .713 .687 .824 r F P 0 g s .38673 .47555 m .36344 .44146 L .40325 .41923 L p .713 .687 .824 r F P 0 g s .50628 .41719 m .52824 .45432 L .48826 .47101 L p .678 .661 .826 r F P 0 g s .48826 .47101 m .46605 .43426 L .50628 .41719 L p .678 .661 .826 r F P 0 g s .38441 .53099 m .40787 .55768 L .36833 .58172 L p .742 .74 .85 r F P 0 g s .36833 .58172 m .34448 .55543 L .38441 .53099 L p .742 .74 .85 r F P 0 g s .25968 .46172 m .28433 .49314 L .24484 .52267 L p .757 .714 .812 r F P 0 g s .24484 .52267 m .2198 .49166 L .25968 .46172 L p .757 .714 .812 r F P 0 g s .75768 .5587 m .77743 .59601 L .73506 .60107 L p .602 .621 .843 r F P 0 g s .73506 .60107 m .7151 .56416 L .75768 .5587 L p .602 .621 .843 r F P 0 g s .52828 .50039 m .55007 .53022 L .50987 .54648 L p .686 .706 .863 r F P 0 g s .50987 .54648 m .48774 .51702 L .52828 .50039 L p .686 .706 .863 r F P 0 g s .69492 .52925 m .7151 .56416 L .67344 .57219 L p .623 .646 .853 r F P 0 g s .67344 .57219 m .653 .53767 L .69492 .52925 L p .623 .646 .853 r F P 0 g s .82 .58401 m .84027 .63337 L .79703 .63537 L p .588 .559 .789 r F P 0 g s .79703 .63537 m .77672 .58651 L .82 .58401 L p .588 .559 .789 r F P 0 g s .82083 .5936 m .84027 .63337 L .79703 .63537 L p .583 .597 .832 r F P 0 g s .79703 .63537 m .77743 .59601 L .82083 .5936 L p .583 .597 .832 r F P 0 g s .29955 .43427 m .32383 .46608 L .28433 .49314 L p .745 .711 .82 r F P 0 g s .28433 .49314 m .25968 .46172 L .29955 .43427 L p .745 .711 .82 r F P 0 g s .42457 .50903 m .44764 .53612 L .40787 .55768 L p .726 .737 .859 r F P 0 g s .40787 .55768 m .38441 .53099 L .42457 .50903 L p .726 .737 .859 r F P 0 g s .67276 .45899 m .69349 .50119 L .65194 .50977 L p .623 .61 .817 r F P 0 g s .65194 .50977 m .63105 .468 L .67276 .45899 L p .623 .61 .817 r F P 0 g s .44336 .39939 m .46605 .43426 L .42624 .45371 L p .698 .682 .831 r F P 0 g s .42624 .45371 m .40325 .41923 L .44336 .39939 L p .698 .682 .831 r F P 0 g s .60989 .42816 m .63105 .468 L .5901 .47946 L p .642 .631 .824 r F P 0 g s .5901 .47946 m .56875 .44004 L .60989 .42816 L p .642 .631 .824 r F P 0 g s .63225 .50512 m .653 .53767 L .61187 .5486 L p .644 .673 .862 r F P 0 g s .61187 .5486 m .59083 .51643 L .63225 .50512 L p .644 .673 .862 r F P 0 g s .73593 .49513 m .75637 .53979 L .71405 .54539 L p .604 .589 .808 r F P 0 g s .71405 .54539 m .69349 .50119 L .73593 .49513 L p .604 .589 .808 r F P 0 g s .54703 .4025 m .56875 .44004 L .52824 .45432 L p .662 .654 .832 r F P 0 g s .52824 .45432 m .50628 .41719 L .54703 .4025 L p .662 .654 .832 r F P 0 g s .33951 .40924 m .36344 .44146 L .32383 .46608 L p .733 .708 .828 r F P 0 g s .32383 .46608 m .29955 .43427 L .33951 .40924 L p .733 .708 .828 r F P 0 g s .27959 .55858 m .30466 .58239 L .26488 .61192 L p .776 .764 .842 r F P 0 g s .26488 .61192 m .23933 .58855 L .27959 .55858 L p .776 .764 .842 r F P 0 g s .79972 .53679 m .82 .58401 L .77672 .58651 L p .587 .569 .8 r F P 0 g s .77672 .58651 m .75637 .53979 L .79972 .53679 L p .587 .569 .8 r F P 0 g s .56937 .48623 m .59083 .51643 L .55007 .53022 L p .667 .7 .871 r F P 0 g s .55007 .53022 m .52828 .50039 L .56937 .48623 L p .667 .7 .871 r F P 0 g s .46505 .48955 m .48774 .51702 L .44764 .53612 L p .709 .732 .869 r F P 0 g s .44764 .53612 m .42457 .50903 L .46505 .48955 L p .709 .732 .869 r F P 0 g s .48387 .38192 m .50628 .41719 L .46605 .43426 L p .682 .676 .838 r F P 0 g s .46605 .43426 m .44336 .39939 L .48387 .38192 L p .682 .676 .838 r F P 0 g s .31985 .53118 m .34448 .55543 L .30466 .58239 L p .763 .763 .852 r F P 0 g s .30466 .58239 m .27959 .55858 L .31985 .53118 L p .763 .763 .852 r F P 0 g s .37966 .38662 m .40325 .41923 L .36344 .44146 L p .718 .704 .836 r F P 0 g s .36344 .44146 m .33951 .40924 L .37966 .38662 L p .718 .704 .836 r F P 0 g s .73773 .52341 m .75768 .5587 L .7151 .56416 L p .601 .636 .858 r F P 0 g s .7151 .56416 m .69492 .52925 L .73773 .52341 L p .601 .636 .858 r F P 0 g s .80128 .55588 m .82083 .5936 L .77743 .59601 L p .581 .61 .847 r F P 0 g s .77743 .59601 m .75768 .5587 L .80128 .55588 L p .581 .61 .847 r F P 0 g s .65179 .41872 m .67276 .45899 L .63105 .468 L p .624 .623 .829 r F P 0 g s .63105 .468 m .60989 .42816 L .65179 .41872 L p .624 .623 .829 r F P 0 g s .23422 .43222 m .25968 .46172 L .2198 .49166 L p .764 .73 .822 r F P 0 g s .2198 .49166 m .19392 .46258 L .23422 .43222 L p .764 .73 .822 r F P 0 g s .67444 .49633 m .69492 .52925 L .653 .53767 L p .622 .663 .869 r F P 0 g s .653 .53767 m .63225 .50512 L .67444 .49633 L p .622 .663 .869 r F P 0 g s .71535 .45248 m .73593 .49513 L .69349 .50119 L p .605 .601 .821 r F P 0 g s .69349 .50119 m .67276 .45899 L .71535 .45248 L p .605 .601 .821 r F P 0 g s .36023 .50632 m .38441 .53099 L .34448 .55543 L p .748 .761 .863 r F P 0 g s .34448 .55543 m .31985 .53118 L .36023 .50632 L p .748 .761 .863 r F P 0 g s .86444 .58421 m .88469 .63412 L .84027 .63337 L p .572 .55 .792 r F P 0 g s .84027 .63337 m .82 .58401 L .86444 .58421 L p .572 .55 .792 r F P 0 g s .86541 .59391 m .88469 .63412 L .84027 .63337 L p .563 .586 .835 r F P 0 g s .84027 .63337 m .82083 .5936 L .86541 .59391 L p .563 .586 .835 r F P 0 g s .5884 .39022 m .60989 .42816 L .56875 .44004 L p .644 .646 .837 r F P 0 g s .56875 .44004 m .54703 .4025 L .5884 .39022 L p .644 .646 .837 r F P 0 g s .50596 .47254 m .52828 .50039 L .48774 .51702 L p .69 .727 .878 r F P 0 g s .48774 .51702 m .46505 .48955 L .50596 .47254 L p .69 .727 .878 r F P 0 g s .2745 .40434 m .29955 .43427 L .25968 .46172 L p .752 .728 .83 r F P 0 g s .25968 .46172 m .23422 .43222 L .2745 .40434 L p .752 .728 .83 r F P 0 g s .42009 .36637 m .44336 .39939 L .40325 .41923 L p .703 .699 .844 r F P 0 g s .40325 .41923 m .37966 .38662 L .42009 .36637 L p .703 .699 .844 r F P 0 g s .77939 .49165 m .79972 .53679 L .75637 .53979 L p .587 .579 .812 r F P 0 g s .75637 .53979 m .73593 .49513 L .77939 .49165 L p .587 .579 .812 r F P 0 g s .6111 .47455 m .63225 .50512 L .59083 .51643 L p .645 .691 .879 r F P 0 g s .59083 .51643 m .56937 .48623 L .6111 .47455 L p .645 .691 .879 r F P 0 g s .52489 .36683 m .54703 .4025 L .50628 .41719 L p .665 .67 .845 r F P 0 g s .50628 .41719 m .48387 .38192 L .52489 .36683 L p .665 .67 .845 r F P 0 g s .40082 .48396 m .42457 .50903 L .38441 .53099 L p .732 .758 .874 r F P 0 g s .38441 .53099 m .36023 .50632 L .40082 .48396 L p .732 .758 .874 r F P 0 g s .31486 .3789 m .33951 .40924 L .29955 .43427 L p .739 .725 .839 r F P 0 g s .29955 .43427 m .2745 .40434 L .31486 .3789 L p .739 .725 .839 r F P 0 g s .84423 .53647 m .86444 .58421 L .82 .58401 L p .57 .559 .803 r F P 0 g s .82 .58401 m .79972 .53679 L .84423 .53647 L p .57 .559 .803 r F P 0 g s .46092 .3485 m .48387 .38192 L .44336 .39939 L p .686 .694 .851 r F P 0 g s .44336 .39939 m .42009 .36637 L .46092 .3485 L p .686 .694 .851 r F P 0 g s .54741 .45799 m .56937 .48623 L .52828 .50039 L p .669 .72 .887 r F P 0 g s .52828 .50039 m .50596 .47254 L .54741 .45799 L p .669 .72 .887 r F P 0 g s .78158 .52019 m .80128 .55588 L .75768 .5587 L p .578 .625 .862 r F P 0 g s .75768 .5587 m .73773 .52341 L .78158 .52019 L p .578 .625 .862 r F P 0 g s .69456 .41177 m .71535 .45248 L .67276 .45899 L p .605 .614 .834 r F P 0 g s .67276 .45899 m .65179 .41872 L .69456 .41177 L p .605 .614 .834 r F P 0 g s .25361 .53686 m .27959 .55858 L .23933 .58855 L p .783 .784 .853 r F P 0 g s .23933 .58855 m .21283 .56731 L .25361 .53686 L p .783 .784 .853 r F P 0 g s .63053 .38035 m .65179 .41872 L .60989 .42816 L p .625 .637 .843 r F P 0 g s .60989 .42816 m .5884 .39022 L .63053 .38035 L p .625 .637 .843 r F P 0 g s .44172 .46407 m .46505 .48955 L .42457 .50903 L p .713 .754 .884 r F P 0 g s .42457 .50903 m .40082 .48396 L .44172 .46407 L p .713 .754 .884 r F P 0 g s .71753 .49011 m .73773 .52341 L .69492 .52925 L p .599 .653 .874 r F P 0 g s .69492 .52925 m .67444 .49633 L .71753 .49011 L p .599 .653 .874 r F P 0 g s .35538 .35586 m .37966 .38662 L .33951 .40924 L p .724 .722 .848 r F P 0 g s .33951 .40924 m .31486 .3789 L .35538 .35586 L p .724 .722 .848 r F P 0 g s .84607 .55577 m .86541 .59391 L .82083 .5936 L p .559 .599 .85 r F P 0 g s .82083 .5936 m .80128 .55588 L .84607 .55577 L p .559 .599 .85 r F P 0 g s .75894 .44852 m .77939 .49165 L .73593 .49513 L p .586 .591 .824 r F P 0 g s .73593 .49513 m .71535 .45248 L .75894 .44852 L p .586 .591 .824 r F P 0 g s .56653 .35413 m .5884 .39022 L .54703 .4025 L p .646 .662 .851 r F P 0 g s .54703 .4025 m .52489 .36683 L .56653 .35413 L p .646 .662 .851 r F P 0 g s .29438 .50901 m .31985 .53118 L .27959 .55858 L p .769 .784 .865 r F P 0 g s .27959 .55858 m .25361 .53686 L .29438 .50901 L p .769 .784 .865 r F P 0 g s .65361 .46538 m .67444 .49633 L .63225 .50512 L p .622 .682 .886 r F P 0 g s .63225 .50512 m .6111 .47455 L .65361 .46538 L p .622 .682 .886 r F P 0 g s .9102 .58722 m .93043 .63771 L .88469 .63412 L p .555 .54 .794 r F P 0 g s .88469 .63412 m .86444 .58421 L .9102 .58722 L p .555 .54 .794 r F P 0 g s .91131 .59704 m .93043 .63771 L .88469 .63412 L p .541 .574 .838 r F P 0 g s .88469 .63412 m .86541 .59391 L .91131 .59704 L p .541 .574 .838 r F P 0 g s .20789 .40464 m .23422 .43222 L .19392 .46258 L p .77 .747 .832 r F P 0 g s .19392 .46258 m .16711 .43546 L .20789 .40464 L p .77 .747 .832 r F P 0 g s .824 .49081 m .84423 .53647 L .79972 .53679 L p .568 .569 .814 r F P 0 g s .79972 .53679 m .77939 .49165 L .824 .49081 L p .568 .569 .814 r F P 0 g s .39619 .33519 m .42009 .36637 L .37966 .38662 L p .708 .717 .857 r F P 0 g s .37966 .38662 m .35538 .35586 L .39619 .33519 L p .708 .717 .857 r F P 0 g s .33524 .4837 m .36023 .50632 L .31985 .53118 L p .754 .782 .876 r F P 0 g s .31985 .53118 m .29438 .50901 L .33524 .4837 L p .754 .782 .876 r F P 0 g s .50225 .33299 m .52489 .36683 L .48387 .38192 L p .668 .687 .859 r F P 0 g s .48387 .38192 m .46092 .3485 L .50225 .33299 L p .668 .687 .859 r F P 0 g s .48304 .44666 m .50596 .47254 L .46505 .48955 L p .693 .749 .894 r F P 0 g s .46505 .48955 m .44172 .46407 L .48304 .44666 L p .693 .749 .894 r F P 0 g s .24862 .37631 m .2745 .40434 L .23422 .43222 L p .758 .746 .841 r F P 0 g s .23422 .43222 m .20789 .40464 L .24862 .37631 L p .758 .746 .841 r F P 0 g s .58951 .44594 m .6111 .47455 L .56937 .48623 L p .645 .712 .896 r F P 0 g s .56937 .48623 m .54741 .45799 L .58951 .44594 L p .645 .712 .896 r F P 0 g s .67352 .37295 m .69456 .41177 L .65179 .41872 L p .604 .628 .848 r F P 0 g s .65179 .41872 m .63053 .38035 L .67352 .37295 L p .604 .628 .848 r F P 0 g s .89005 .53891 m .9102 .58722 L .86444 .58421 L p .552 .549 .805 r F P 0 g s .86444 .58421 m .84423 .53647 L .89005 .53891 L p .552 .549 .805 r F P 0 g s .2894 .35042 m .31486 .3789 L .2745 .40434 L p .745 .744 .851 r F P 0 g s .2745 .40434 m .24862 .37631 L .2894 .35042 L p .745 .744 .851 r F P 0 g s .37629 .4609 m .40082 .48396 L .36023 .50632 L p .737 .78 .888 r F P 0 g s .36023 .50632 m .33524 .4837 L .37629 .4609 L p .737 .78 .888 r F P 0 g s .73834 .40734 m .75894 .44852 L .71535 .45248 L p .584 .603 .838 r F P 0 g s .71535 .45248 m .69456 .41177 L .73834 .40734 L p .584 .603 .838 r F P 0 g s .76166 .4865 m .78158 .52019 L .73773 .52341 L p .574 .641 .879 r F P 0 g s .73773 .52341 m .71753 .49011 L .76166 .4865 L p .574 .641 .879 r F P 0 g s .60891 .34383 m .63053 .38035 L .5884 .39022 L p .626 .653 .857 r F P 0 g s .5884 .39022 m .56653 .35413 L .60891 .34383 L p .626 .653 .857 r F P 0 g s .8266 .51967 m .84607 .55577 L .80128 .55588 L p .554 .613 .866 r F P 0 g s .80128 .55588 m .78158 .52019 L .8266 .51967 L p .554 .613 .866 r F P 0 g s .43737 .31689 m .46092 .3485 L .42009 .36637 L p .69 .712 .865 r F P 0 g s .42009 .36637 m .39619 .33519 L .43737 .31689 L p .69 .712 .865 r F P 0 g s .69703 .45878 m .71753 .49011 L .67444 .49633 L p .596 .671 .892 r F P 0 g s .67444 .49633 m .65361 .46538 L .69703 .45878 L p .596 .671 .892 r F P 0 g s .80369 .44719 m .824 .49081 L .77939 .49165 L p .566 .58 .827 r F P 0 g s .77939 .49165 m .75894 .44852 L .80369 .44719 L p .566 .58 .827 r F P 0 g s .89217 .55847 m .91131 .59704 L .86541 .59391 L p .535 .586 .853 r F P 0 g s .86541 .59391 m .84607 .55577 L .89217 .55847 L p .535 .586 .853 r F P 0 g s .52489 .43173 m .54741 .45799 L .50596 .47254 L p .67 .742 .904 r F P 0 g s .50596 .47254 m .48304 .44666 L .52489 .43173 L p .67 .742 .904 r F P 0 g s .54419 .31986 m .56653 .35413 L .52489 .36683 L p .648 .679 .866 r F P 0 g s .52489 .36683 m .50225 .33299 L .54419 .31986 L p .648 .679 .866 r F P 0 g s .33035 .32693 m .35538 .35586 L .31486 .3789 L p .729 .74 .86 r F P 0 g s .31486 .3789 m .2894 .35042 L .33035 .32693 L p .729 .74 .86 r F P 0 g s .41765 .4406 m .44172 .46407 L .40082 .48396 L p .717 .777 .899 r F P 0 g s .40082 .48396 m .37629 .4609 L .41765 .4406 L p .717 .777 .899 r F P 0 g s .22663 .51729 m .25361 .53686 L .21283 .56731 L p .79 .805 .865 r F P 0 g s .21283 .56731 m .18529 .54825 L .22663 .51729 L p .79 .805 .865 r F P 0 g s .63237 .4364 m .65361 .46538 L .6111 .47455 L p .62 .702 .903 r F P 0 g s .6111 .47455 m .58951 .44594 L .63237 .4364 L p .62 .702 .903 r F P 0 g s .95744 .59314 m .97765 .64426 L .93043 .63771 L p .537 .53 .795 r F P 0 g s .93043 .63771 m .9102 .58722 L .95744 .59314 L p .537 .53 .795 r F P 0 g s .95871 .60311 m .97765 .64426 L .93043 .63771 L p .518 .562 .839 r F P 0 g s .93043 .63771 m .91131 .59704 L .95871 .60311 L p .518 .562 .839 r F P 0 g s .86991 .49272 m .89005 .53891 L .84423 .53647 L p .549 .559 .817 r F P 0 g s .84423 .53647 m .824 .49081 L .86991 .49272 L p .549 .559 .817 r F P 0 g s .26794 .48894 m .29438 .50901 L .25361 .53686 L p .776 .806 .877 r F P 0 g s .25361 .53686 m .22663 .51729 L .26794 .48894 L p .776 .806 .877 r F P 0 g s .18056 .37898 m .20789 .40464 L .16711 .43546 L p .777 .765 .842 r F P 0 g s .16711 .43546 m .13927 .41029 L .18056 .37898 L p .777 .765 .842 r F P 0 g s .47905 .30096 m .50225 .33299 L .46092 .3485 L p .671 .705 .873 r F P 0 g s .46092 .3485 m .43737 .31689 L .47905 .30096 L p .671 .705 .873 r F P 0 g s .37156 .30583 m .39619 .33519 L .35538 .35586 L p .712 .736 .87 r F P 0 g s .35538 .35586 m .33035 .32693 L .37156 .30583 L p .712 .736 .87 r F P 0 g s .71751 .36807 m .73834 .40734 L .69456 .41177 L p .583 .617 .852 r F P 0 g s .69456 .41177 m .67352 .37295 L .71751 .36807 L p .583 .617 .852 r F P 0 g s .65216 .336 m .67352 .37295 L .63053 .38035 L p .604 .643 .862 r F P 0 g s .63053 .38035 m .60891 .34383 L .65216 .336 L p .604 .643 .862 r F P 0 g s .22179 .35017 m .24862 .37631 L .20789 .40464 L p .765 .765 .852 r F P 0 g s .20789 .40464 m .18056 .37898 L .22179 .35017 L p .765 .765 .852 r F P 0 g s .56738 .41929 m .58951 .44594 L .54741 .45799 L p .645 .733 .913 r F P 0 g s .54741 .45799 m .52489 .43173 L .56738 .41929 L p .645 .733 .913 r F P 0 g s .45942 .42279 m .48304 .44666 L .44172 .46407 L p .695 .772 .91 r F P 0 g s .44172 .46407 m .41765 .4406 L .45942 .42279 L p .695 .772 .91 r F P 0 g s .30933 .46316 m .33524 .4837 L .29438 .50901 L p .759 .805 .89 r F P 0 g s .29438 .50901 m .26794 .48894 L .30933 .46316 L p .759 .805 .89 r F P 0 g s .78326 .40553 m .80369 .44719 L .75894 .44852 L p .563 .592 .841 r F P 0 g s .75894 .44852 m .73834 .40734 L .78326 .40553 L p .563 .592 .841 r F P 0 g s .80697 .48559 m .8266 .51967 L .78158 .52019 L p .548 .628 .883 r F P 0 g s .78158 .52019 m .76166 .4865 L .80697 .48559 L p .548 .628 .883 r F P 0 g s .58687 .30914 m .60891 .34383 L .56653 .35413 L p .626 .67 .872 r F P 0 g s .56653 .35413 m .54419 .31986 L .58687 .30914 L p .626 .67 .872 r F P 0 g s .74147 .4548 m .76166 .4865 L .71753 .49011 L p .57 .658 .897 r F P 0 g s .71753 .49011 m .69703 .45878 L .74147 .4548 L p .57 .658 .897 r F P 0 g s .93734 .54424 m .95744 .59314 L .9102 .58722 L p .533 .538 .806 r F P 0 g s .9102 .58722 m .89005 .53891 L .93734 .54424 L p .533 .538 .806 r F P 0 g s .87295 .52195 m .89217 .55847 L .84607 .55577 L p .528 .599 .869 r F P 0 g s .84607 .55577 m .8266 .51967 L .87295 .52195 L p .528 .599 .869 r F P 0 g s .26305 .3238 m .2894 .35042 L .24862 .37631 L p .75 .763 .863 r F P 0 g s .24862 .37631 m .22179 .35017 L .26305 .3238 L p .75 .763 .863 r F P 0 g s .84974 .44857 m .86991 .49272 L .824 .49081 L p .545 .569 .83 r F P 0 g s .824 .49081 m .80369 .44719 L .84974 .44857 L p .545 .569 .83 r F P 0 g s .41313 .28709 m .43737 .31689 L .39619 .33519 L p .694 .731 .879 r F P 0 g s .39619 .33519 m .37156 .30583 L .41313 .28709 L p .694 .731 .879 r F P 0 g s .67614 .42942 m .69703 .45878 L .65361 .46538 L p .593 .69 .91 r F P 0 g s .65361 .46538 m .63237 .4364 L .67614 .42942 L p .593 .69 .91 r F P 0 g s .3509 .43991 m .37629 .4609 L .33524 .4837 L p .741 .804 .902 r F P 0 g s .33524 .4837 m .30933 .46316 L .3509 .43991 L p .741 .804 .902 r F P 0 g s .93977 .56408 m .95871 .60311 L .91131 .59704 L p .511 .573 .854 r F P 0 g s .91131 .59704 m .89217 .55847 L .93977 .56408 L p .511 .573 .854 r F P 0 g s .52133 .2874 m .54419 .31986 L .50225 .33299 L p .649 .697 .881 r F P 0 g s .50225 .33299 m .47905 .30096 L .52133 .2874 L p .649 .697 .881 r F P 0 g s .50172 .40746 m .52489 .43173 L .48304 .44666 L p .671 .765 .921 r F P 0 g s .48304 .44666 m .45942 .42279 L .50172 .40746 L p .671 .765 .921 r F P 0 g s .30445 .29985 m .33035 .32693 L .2894 .35042 L p .735 .76 .873 r F P 0 g s .2894 .35042 m .26305 .3238 L .30445 .29985 L p .735 .76 .873 r F P 0 g s .61065 .40938 m .63237 .4364 L .58951 .44594 L p .618 .723 .921 r F P 0 g s .58951 .44594 m .56738 .41929 L .61065 .40938 L p .618 .723 .921 r F P 0 g s .9173 .49747 m .93734 .54424 L .89005 .53891 L p .529 .547 .819 r F P 0 g s .89005 .53891 m .86991 .49272 L .9173 .49747 L p .529 .547 .819 r F P 0 g s .39276 .41917 m .41765 .4406 L .37629 .4609 L p .72 .8 .915 r F P 0 g s .37629 .4609 m .3509 .43991 L .39276 .41917 L p .72 .8 .915 r F P 0 g s .6964 .33067 m .71751 .36807 L .67352 .37295 L p .581 .632 .867 r F P 0 g s .67352 .37295 m .65216 .336 L .6964 .33067 L p .581 .632 .867 r F P 0 g s .76265 .36578 m .78326 .40553 L .73834 .40734 L p .56 .606 .855 r F P 0 g s .73834 .40734 m .71751 .36807 L .76265 .36578 L p .56 .606 .855 r F P 0 g s .4552 .27072 m .47905 .30096 L .43737 .31689 L p .673 .725 .888 r F P 0 g s .43737 .31689 m .41313 .28709 L .4552 .27072 L p .673 .725 .888 r F P 0 g s .63042 .30087 m .65216 .336 L .60891 .34383 L p .603 .66 .878 r F P 0 g s .60891 .34383 m .58687 .30914 L .63042 .30087 L p .603 .66 .878 r F P 0 g s .19853 .4999 m .22663 .51729 L .18529 .54825 L p .796 .827 .876 r F P 0 g s .18529 .54825 m .15658 .53141 L .19853 .4999 L p .796 .827 .876 r F P 0 g s .34611 .27829 m .37156 .30583 L .33035 .32693 L p .717 .756 .884 r F P 0 g s .33035 .32693 m .30445 .29985 L .34611 .27829 L p .717 .756 .884 r F P 0 g s .15214 .35526 m .18056 .37898 L .13927 .41029 L p .784 .784 .853 r F P 0 g s .13927 .41029 m .11029 .3871 L .15214 .35526 L p .784 .784 .853 r F P 0 g s .82949 .4064 m .84974 .44857 L .80369 .44719 L p .541 .581 .843 r F P 0 g s .80369 .44719 m .78326 .40553 L .82949 .4064 L p .541 .581 .843 r F P 0 g s .7871 .45351 m .80697 .48559 L .76166 .4865 L p .541 .644 .901 r F P 0 g s .76166 .4865 m .74147 .4548 L .7871 .45351 L p .541 .644 .901 r F P 0 g s .8536 .48747 m .87295 .52195 L .8266 .51967 L p .52 .613 .886 r F P 0 g s .8266 .51967 m .80697 .48559 L .8536 .48747 L p .52 .613 .886 r F P 0 g s .24044 .47103 m .26794 .48894 L .22663 .51729 L p .781 .829 .889 r F P 0 g s .22663 .51729 m .19853 .4999 L .24044 .47103 L p .781 .829 .889 r F P 0 g s .56435 .27625 m .58687 .30914 L .54419 .31986 L p .626 .688 .888 r F P 0 g s .54419 .31986 m .52133 .2874 L .56435 .27625 L p .626 .688 .888 r F P 0 g s .54465 .39464 m .56738 .41929 L .52489 .43173 L p .643 .756 .931 r F P 0 g s .52489 .43173 m .50172 .40746 L .54465 .39464 L p .643 .756 .931 r F P 0 g s .72095 .42507 m .74147 .4548 L .69703 .45878 L p .563 .677 .915 r F P 0 g s .69703 .45878 m .67614 .42942 L .72095 .42507 L p .563 .677 .915 r F P 0 g s .1939 .32593 m .22179 .35017 L .18056 .37898 L p .771 .784 .864 r F P 0 g s .18056 .37898 m .15214 .35526 L .1939 .32593 L p .771 .784 .864 r F P 0 g s .9208 .52714 m .93977 .56408 L .89217 .55847 L p .502 .585 .87 r F P 0 g s .89217 .55847 m .87295 .52195 L .9208 .52714 L p .502 .585 .87 r F P 0 g s .43503 .40094 m .45942 .42279 L .41765 .4406 L p .696 .796 .927 r F P 0 g s .41765 .4406 m .39276 .41917 L .43503 .40094 L p .696 .796 .927 r F P 0 g s .2824 .44475 m .30933 .46316 L .26794 .48894 L p .764 .829 .903 r F P 0 g s .26794 .48894 m .24044 .47103 L .2824 .44475 L p .764 .829 .903 r F P 0 g s .89726 .45277 m .9173 .49747 L .86991 .49272 L p .524 .557 .831 r F P 0 g s .86991 .49272 m .84974 .44857 L .89726 .45277 L p .524 .557 .831 r F P 0 g s .65482 .40204 m .67614 .42942 L .63237 .4364 L p .588 .711 .928 r F P 0 g s .63237 .4364 m .61065 .40938 L .65482 .40204 L p .588 .711 .928 r F P 0 g s .23568 .29907 m .26305 .3238 L .22179 .35017 L p .756 .783 .875 r F P 0 g s .22179 .35017 m .1939 .32593 L .23568 .29907 L p .756 .783 .875 r F P 0 g s .38812 .2591 m .41313 .28709 L .37156 .30583 L p .697 .751 .894 r F P 0 g s .37156 .30583 m .34611 .27829 L .38812 .2591 L p .697 .751 .894 r F P 0 g s .49786 .25673 m .52133 .2874 L .47905 .30096 L p .651 .717 .896 r F P 0 g s .47905 .30096 m .4552 .27072 L .49786 .25673 L p .651 .717 .896 r F P 0 g s .32454 .42102 m .3509 .43991 L .30933 .46316 L p .744 .828 .916 r F P 0 g s .30933 .46316 m .2824 .44475 L .32454 .42102 L p .744 .828 .916 r F P 0 g s .7418 .32791 m .76265 .36578 L .71751 .36807 L p .557 .62 .871 r F P 0 g s .71751 .36807 m .6964 .33067 L .7418 .32791 L p .557 .62 .871 r F P 0 g s .67496 .29509 m .6964 .33067 L .65216 .336 L p .578 .648 .883 r F P 0 g s .65216 .336 m .63042 .30087 L .67496 .29509 L p .578 .648 .883 r F P 0 g s .27759 .27463 m .30445 .29985 L .26305 .3238 L p .74 .781 .886 r F P 0 g s .26305 .3238 m .23568 .29907 L .27759 .27463 L p .74 .781 .886 r F P 0 g s .47781 .3852 m .50172 .40746 L .45942 .42279 L p .67 .789 .938 r F P 0 g s .45942 .42279 m .43503 .40094 L .47781 .3852 L p .67 .789 .938 r F P 0 g s .80909 .36616 m .82949 .4064 L .78326 .40553 L p .537 .593 .858 r F P 0 g s .78326 .40553 m .76265 .36578 L .80909 .36616 L p .537 .593 .858 r F P 0 g s .58836 .38435 m .61065 .40938 L .56738 .41929 L p .613 .745 .939 r F P 0 g s .56738 .41929 m .54465 .39464 L .58836 .38435 L p .613 .745 .939 r F P 0 g s .60822 .26754 m .63042 .30087 L .58687 .30914 L p .602 .677 .894 r F P 0 g s .58687 .30914 m .56435 .27625 L .60822 .26754 L p .602 .677 .894 r F P 0 g s .43061 .24229 m .4552 .27072 L .41313 .28709 L p .675 .745 .903 r F P 0 g s .41313 .28709 m .38812 .2591 L .43061 .24229 L p .675 .745 .903 r F P 0 g s .83407 .455 m .8536 .48747 L .80697 .48559 L p .511 .629 .903 r F P 0 g s .80697 .48559 m .7871 .45351 L .83407 .455 L p .511 .629 .903 r F P 0 g s .87718 .41007 m .89726 .45277 L .84974 .44857 L p .518 .568 .845 r F P 0 g s .84974 .44857 m .82949 .4064 L .87718 .41007 L p .518 .568 .845 r F P 0 g s .76695 .42341 m .7871 .45351 L .74147 .4548 L p .532 .662 .919 r F P 0 g s .74147 .4548 m .72095 .42507 L .76695 .42341 L p .532 .662 .919 r F P 0 g s .36695 .39983 m .39276 .41917 L .3509 .43991 L p .721 .825 .929 r F P 0 g s .3509 .43991 m .32454 .42102 L .36695 .39983 L p .721 .825 .929 r F P 0 g s .90175 .49225 m .9208 .52714 L .87295 .52195 L p .492 .598 .887 r F P 0 g s .87295 .52195 m .8536 .48747 L .90175 .49225 L p .492 .598 .887 r F P 0 g s .54125 .24515 m .56435 .27625 L .52133 .2874 L p .626 .707 .904 r F P 0 g s .52133 .2874 m .49786 .25673 L .54125 .24515 L p .626 .707 .904 r F P 0 g s .31974 .25259 m .34611 .27829 L .30445 .29985 L p .721 .778 .897 r F P 0 g s .30445 .29985 m .27759 .27463 L .31974 .25259 L p .721 .778 .897 r F P 0 g s .16919 .48476 m .19853 .4999 L .15658 .53141 L p .802 .85 .887 r F P 0 g s .15658 .53141 m .12656 .51686 L .16919 .48476 L p .802 .85 .887 r F P 0 g s .12249 .33351 m .15214 .35526 L .11029 .3871 L p .79 .804 .863 r F P 0 g s .11029 .3871 m .08003 .36592 L .12249 .33351 L p .79 .804 .863 r F P 0 g s .70003 .39732 m .72095 .42507 L .67614 .42942 L p .556 .696 .934 r F P 0 g s .67614 .42942 m .65482 .40204 L .70003 .39732 L p .556 .696 .934 r F P 0 g s .52124 .37199 m .54465 .39464 L .50172 .40746 L p .64 .78 .948 r F P 0 g s .50172 .40746 m .47781 .3852 L .52124 .37199 L p .64 .78 .948 r F P 0 g s .21174 .45533 m .24044 .47103 L .19853 .4999 L p .786 .852 .901 r F P 0 g s .19853 .4999 m .16919 .48476 L .21174 .45533 L p .786 .852 .901 r F P 0 g s .16485 .30363 m .1939 .32593 L .15214 .35526 L p .777 .804 .875 r F P 0 g s .15214 .35526 m .12249 .33351 L .16485 .30363 L p .777 .804 .875 r F P 0 g s .40975 .38115 m .43503 .40094 L .39276 .41917 L p .696 .82 .942 r F P 0 g s .39276 .41917 m .36695 .39983 L .40975 .38115 L p .696 .82 .942 r F P 0 g s .72065 .29188 m .7418 .32791 L .6964 .33067 L p .552 .635 .887 r F P 0 g s .6964 .33067 m .67496 .29509 L .72065 .29188 L p .552 .635 .887 r F P 0 g s .63298 .37664 m .65482 .40204 L .61065 .40938 L p .581 .732 .947 r F P 0 g s .61065 .40938 m .58836 .38435 L .63298 .37664 L p .581 .732 .947 r F P 0 g s .47369 .22785 m .49786 .25673 L .4552 .27072 L p .651 .737 .912 r F P 0 g s .4552 .27072 m .43061 .24229 L .47369 .22785 L p .651 .737 .912 r F P 0 g s .7885 .32782 m .80909 .36616 L .76265 .36578 L p .531 .607 .874 r F P 0 g s .76265 .36578 m .7418 .32791 L .7885 .32782 L p .531 .607 .874 r F P 0 g s .36223 .23293 m .38812 .2591 L .34611 .27829 L p .7 .773 .908 r F P 0 g s .34611 .27829 m .31974 .25259 L .36223 .23293 L p .7 .773 .908 r F P 0 g s .6531 .26132 m .67496 .29509 L .63042 .30087 L p .575 .665 .899 r F P 0 g s .63042 .30087 m .60822 .26754 L .6531 .26132 L p .575 .665 .899 r F P 0 g s .25433 .42852 m .2824 .44475 L .24044 .47103 L p .767 .853 .915 r F P 0 g s .24044 .47103 m .21174 .45533 L .25433 .42852 L p .767 .853 .915 r F P 0 g s .2072 .27624 m .23568 .29907 L .1939 .32593 L p .761 .804 .887 r F P 0 g s .1939 .32593 m .16485 .30363 L .2072 .27624 L p .761 .804 .887 r F P 0 g s .85701 .36932 m .87718 .41007 L .82949 .4064 L p .512 .58 .86 r F P 0 g s .82949 .4064 m .80909 .36616 L .85701 .36932 L p .512 .58 .86 r F P 0 g s .5855 .236 m .60822 .26754 L .56435 .27625 L p .6 .696 .911 r F P 0 g s .56435 .27625 m .54125 .24515 L .5855 .236 L p .6 .696 .911 r F P 0 g s .81429 .42454 m .83407 .455 L .7871 .45351 L p .499 .645 .921 r F P 0 g s .7871 .45351 m .76695 .42341 L .81429 .42454 L p .499 .645 .921 r F P 0 g s .29708 .40429 m .32454 .42102 L .2824 .44475 L p .746 .852 .929 r F P 0 g s .2824 .44475 m .25433 .42852 L .29708 .40429 L p .746 .852 .929 r F P 0 g s .88256 .45939 m .90175 .49225 L .8536 .48747 L p .479 .612 .905 r F P 0 g s .8536 .48747 m .83407 .455 L .88256 .45939 L p .479 .612 .905 r F P 0 g s .24965 .25128 m .27759 .27463 L .23568 .29907 L p .744 .802 .899 r F P 0 g s .23568 .29907 m .2072 .27624 L .24965 .25128 L p .744 .802 .899 r F P 0 g s .56543 .36132 m .58836 .38435 L .54465 .39464 L p .607 .768 .957 r F P 0 g s .54465 .39464 m .52124 .37199 L .56543 .36132 L p .607 .768 .957 r F P 0 g s .45307 .365 m .47781 .3852 L .43503 .40094 L p .667 .814 .954 r F P 0 g s .43503 .40094 m .40975 .38115 L .45307 .365 L p .667 .814 .954 r F P 0 g s .74644 .3953 m .76695 .42341 L .72095 .42507 L p .521 .68 .938 r F P 0 g s .72095 .42507 m .70003 .39732 L .74644 .3953 L p .521 .68 .938 r F P 0 g s .40519 .21565 m .43061 .24229 L .38812 .2591 L p .677 .767 .919 r F P 0 g s .38812 .2591 m .36223 .23293 L .40519 .21565 L p .677 .767 .919 r F P 0 g s .51751 .21582 m .54125 .24515 L .49786 .25673 L p .625 .727 .921 r F P 0 g s .49786 .25673 m .47369 .22785 L .51751 .21582 L p .625 .727 .921 r F P 0 g s .67864 .37156 m .70003 .39732 L .65482 .40204 L p .545 .717 .952 r F P 0 g s .65482 .40204 m .63298 .37664 L .67864 .37156 L p .545 .717 .952 r F P 0 g s .34009 .38262 m .36695 .39983 L .32454 .42102 L p .721 .85 .943 r F P 0 g s .32454 .42102 m .29708 .40429 L .34009 .38262 L p .721 .85 .943 r F P 0 g s .29233 .22874 m .31974 .25259 L .27759 .27463 L p .724 .799 .911 r F P 0 g s .27759 .27463 m .24965 .25128 L .29233 .22874 L p .724 .799 .911 r F P 0 g s .76765 .29132 m .7885 .32782 L .7418 .32791 L p .525 .621 .89 r F P 0 g s .7418 .32791 m .72065 .29188 L .76765 .29132 L p .525 .621 .89 r F P 0 g s .69913 .25766 m .72065 .29188 L .67496 .29509 L p .547 .652 .903 r F P 0 g s .67496 .29509 m .6531 .26132 L .69913 .25766 L p .547 .652 .903 r F P 0 g s .09149 .31378 m .12249 .33351 L .08003 .36592 L p .796 .824 .873 r F P 0 g s .08003 .36592 m .04836 .3468 L .09149 .31378 L p .796 .824 .873 r F P 0 g s .83668 .33048 m .85701 .36932 L .80909 .36616 L p .505 .592 .875 r F P 0 g s .80909 .36616 m .7885 .32782 L .83668 .33048 L p .505 .592 .875 r F P 0 g s .13845 .47196 m .16919 .48476 L .12656 .51686 L p .806 .873 .896 r F P 0 g s .12656 .51686 m .0951 .5047 L .13845 .47196 L p .806 .873 .896 r F P 0 g s .49703 .35139 m .52124 .37199 L .47781 .3852 L p .634 .804 .964 r F P 0 g s .47781 .3852 m .45307 .365 L .49703 .35139 L p .634 .804 .964 r F P 0 g s .63076 .22934 m .6531 .26132 L .60822 .26754 L p .571 .683 .916 r F P 0 g s .60822 .26754 m .5855 .236 L .63076 .22934 L p .571 .683 .916 r F P 0 g s .13448 .28331 m .16485 .30363 L .12249 .33351 L p .782 .825 .886 r F P 0 g s .12249 .33351 m .09149 .31378 L .13448 .28331 L p .782 .825 .886 r F P 0 g s .44874 .20076 m .47369 .22785 L .43061 .24229 L p .651 .759 .928 r F P 0 g s .43061 .24229 m .40519 .21565 L .44874 .20076 L p .651 .759 .928 r F P 0 g s .61053 .35325 m .63298 .37664 L .58836 .38435 L p .571 .754 .964 r F P 0 g s .58836 .38435 m .56543 .36132 L .61053 .35325 L p .571 .754 .964 r F P 0 g s .18171 .44194 m .21174 .45533 L .16919 .48476 L p .789 .876 .911 r F P 0 g s .16919 .48476 m .13845 .47196 L .18171 .44194 L p .789 .876 .911 r F P 0 g s .38349 .36349 m .40975 .38115 L .36695 .39983 L p .693 .845 .956 r F P 0 g s .36695 .39983 m .34009 .38262 L .38349 .36349 L p .693 .845 .956 r F P 0 g s .33535 .20859 m .36223 .23293 L .31974 .25259 L p .702 .795 .922 r F P 0 g s .31974 .25259 m .29233 .22874 L .33535 .20859 L p .702 .795 .922 r F P 0 g s .56218 .20623 m .5855 .236 L .54125 .24515 L p .596 .716 .928 r F P 0 g s .54125 .24515 m .51751 .21582 L .56218 .20623 L p .596 .716 .928 r F P 0 g s .17745 .25535 m .2072 .27624 L .16485 .30363 L p .766 .825 .898 r F P 0 g s .16485 .30363 m .13448 .28331 L .17745 .25535 L p .766 .825 .898 r F P 0 g s .86317 .42857 m .88256 .45939 L .83407 .455 L p .465 .626 .922 r F P 0 g s .83407 .455 m .81429 .42454 L .86317 .42857 L p .465 .626 .922 r F P 0 g s .79421 .39608 m .81429 .42454 L .76695 .42341 L p .485 .661 .939 r F P 0 g s .76695 .42341 m .74644 .3953 L .79421 .39608 L p .485 .661 .939 r F P 0 g s .22499 .41456 m .25433 .42852 L .21174 .45533 L p .769 .877 .926 r F P 0 g s .21174 .45533 m .18171 .44194 L .22499 .41456 L p .769 .877 .926 r F P 0 g s .72551 .3692 m .74644 .3953 L .70003 .39732 L p .508 .699 .955 r F P 0 g s .70003 .39732 m .67864 .37156 L .72551 .3692 L p .508 .699 .955 r F P 0 g s .54176 .34034 m .56543 .36132 L .52124 .37199 L p .598 .792 .973 r F P 0 g s .52124 .37199 m .49703 .35139 L .54176 .34034 L p .598 .792 .973 r F P 0 g s .22051 .22984 m .24965 .25128 L .2072 .27624 L p .748 .824 .911 r F P 0 g s .2072 .27624 m .17745 .25535 L .22051 .22984 L p .748 .824 .911 r F P 0 g s .42739 .34691 m .45307 .365 L .40975 .38115 L p .661 .838 .968 r F P 0 g s .40975 .38115 m .38349 .36349 L .42739 .34691 L p .661 .838 .968 r F P 0 g s .37883 .19083 m .40519 .21565 L .36223 .23293 L p .677 .789 .933 r F P 0 g s .36223 .23293 m .33535 .20859 L .37883 .19083 L p .677 .789 .933 r F P 0 g s .2684 .3898 m .29708 .40429 L .25433 .42852 L p .746 .877 .94 r F P 0 g s .25433 .42852 m .22499 .41456 L .2684 .3898 L p .746 .877 .94 r F P 0 g s .49301 .18828 m .51751 .21582 L .47369 .22785 L p .623 .749 .937 r F P 0 g s .47369 .22785 m .44874 .20076 L .49301 .18828 L p .623 .749 .937 r F P 0 g s .74648 .25664 m .76765 .29132 L .72065 .29188 L p .518 .637 .906 r F P 0 g s .72065 .29188 m .69913 .25766 L .74648 .25664 L p .518 .637 .906 r F P 0 g s .81614 .29351 m .83668 .33048 L .7885 .32782 L p .497 .606 .891 r F P 0 g s .7885 .32782 m .76765 .29132 L .81614 .29351 L p .497 .606 .891 r F P 0 g s .67717 .22523 m .69913 .25766 L .6531 .26132 L p .541 .669 .921 r F P 0 g s .6531 .26132 m .63076 .22934 L .67717 .22523 L p .541 .669 .921 r F P 0 g s .6567 .34782 m .67864 .37156 L .63298 .37664 L p .532 .737 .969 r F P 0 g s .63298 .37664 m .61053 .35325 L .6567 .34782 L p .532 .737 .969 r F P 0 g s .26377 .20677 m .29233 .22874 L .24965 .25128 L p .727 .822 .924 r F P 0 g s .24965 .25128 m .22051 .22984 L .26377 .20677 L p .727 .822 .924 r F P 0 g s .60786 .19913 m .63076 .22934 L .5855 .236 L p .566 .702 .933 r F P 0 g s .5855 .236 m .56218 .20623 L .60786 .19913 L p .566 .702 .933 r F P 0 g s .31206 .36762 m .34009 .38262 L .29708 .40429 L p .719 .874 .954 r F P 0 g s .29708 .40429 m .2684 .3898 L .31206 .36762 L p .719 .874 .954 r F P 0 g s .47193 .33289 m .49703 .35139 L .45307 .365 L p .625 .828 .978 r F P 0 g s .45307 .365 m .42739 .34691 L .47193 .33289 L p .625 .828 .978 r F P 0 g s .42289 .17547 m .44874 .20076 L .40519 .21565 L p .65 .781 .944 r F P 0 g s .40519 .21565 m .37883 .19083 L .42289 .17547 L p .65 .781 .944 r F P 0 g s .58741 .3319 m .61053 .35325 L .56543 .36132 L p .558 .776 .98 r F P 0 g s .56543 .36132 m .54176 .34034 L .58741 .3319 L p .558 .776 .98 r F P 0 g s .84353 .39977 m .86317 .42857 L .81429 .42454 L p .447 .641 .939 r F P 0 g s .81429 .42454 m .79421 .39608 L .84353 .39977 L p .447 .641 .939 r F P 0 g s .10616 .4616 m .13845 .47196 L .0951 .5047 L p .809 .896 .904 r F P 0 g s .0951 .5047 m .06202 .49501 L .10616 .4616 L p .809 .896 .904 r F P 0 g s .53815 .17824 m .56218 .20623 L .51751 .21582 L p .592 .737 .944 r F P 0 g s .51751 .21582 m .49301 .18828 L .53815 .17824 L p .592 .737 .944 r F P 0 g s .30737 .1861 m .33535 .20859 L .29233 .22874 L p .703 .817 .936 r F P 0 g s .29233 .22874 m .26377 .20677 L .30737 .1861 L p .703 .817 .936 r F P 0 g s .77376 .36965 m .79421 .39608 L .74644 .3953 L p .468 .678 .957 r F P 0 g s .74644 .3953 m .72551 .3692 L .77376 .36965 L p .468 .678 .957 r F P 0 g s .3561 .34802 m .38349 .36349 L .34009 .38262 L p .688 .869 .967 r F P 0 g s .34009 .38262 m .31206 .36762 L .3561 .34802 L p .688 .869 .967 r F P 0 g s .15019 .43093 m .18171 .44194 L .13845 .47196 L p .79 .899 .919 r F P 0 g s .13845 .47196 m .10616 .4616 L .15019 .43093 L p .79 .899 .919 r F P 0 g s .70408 .34513 m .72551 .3692 L .67864 .37156 L p .491 .717 .972 r F P 0 g s .67864 .37156 m .6567 .34782 L .70408 .34513 L p .491 .717 .972 r F P 0 g s .79533 .25837 m .81614 .29351 L .76765 .29132 L p .487 .62 .908 r F P 0 g s .76765 .29132 m .74648 .25664 L .79533 .25837 L p .487 .62 .908 r F P 0 g s .72492 .22377 m .74648 .25664 L .69913 .25766 L p .509 .653 .923 r F P 0 g s .69913 .25766 m .67717 .22523 L .72492 .22377 L p .509 .653 .923 r F P 0 g s .1942 .40295 m .22499 .41456 L .18171 .44194 L p .768 .901 .934 r F P 0 g s .18171 .44194 m .15019 .43093 L .1942 .40295 L p .768 .901 .934 r F P 0 g s .51725 .32145 m .54176 .34034 L .49703 .35139 L p .586 .814 .986 r F P 0 g s .49703 .35139 m .47193 .33289 L .51725 .32145 L p .586 .814 .986 r F P 0 g s .46767 .16253 m .49301 .18828 L .44874 .20076 L p .619 .77 .953 r F P 0 g s .44874 .20076 m .42289 .17547 L .46767 .16253 L p .619 .77 .953 r F P 0 g s .6547 .19459 m .67717 .22523 L .63076 .22934 L p .533 .687 .937 r F P 0 g s .63076 .22934 m .60786 .19913 L .6547 .19459 L p .533 .687 .937 r F P 0 g s .35141 .16785 m .37883 .19083 L .33535 .20859 L p .676 .811 .948 r F P 0 g s .33535 .20859 m .30737 .1861 L .35141 .16785 L p .676 .811 .948 r F P 0 g s .40064 .33099 m .42739 .34691 L .38349 .36349 L p .653 .861 .979 r F P 0 g s .38349 .36349 m .3561 .34802 L .40064 .33099 L p .653 .861 .979 r F P 0 g s .63412 .32614 m .6567 .34782 L .61053 .35325 L p .516 .757 .984 r F P 0 g s .61053 .35325 m .58741 .3319 L .63412 .32614 L p .516 .757 .984 r F P 0 g s .23834 .37763 m .2684 .3898 L .22499 .41456 L p .743 .9 .949 r F P 0 g s .22499 .41456 m .1942 .40295 L .23834 .37763 L p .743 .9 .949 r F P 0 g s .5843 .1707 m .60786 .19913 L .56218 .20623 L p .559 .722 .95 r F P 0 g s .56218 .20623 m .53815 .17824 L .5843 .1707 L p .559 .722 .95 r F P 0 g s .82357 .37302 m .84353 .39977 L .79421 .39608 L p .426 .656 .955 r F P 0 g s .79421 .39608 m .77376 .36965 L .82357 .37302 L p .426 .656 .955 r F P 0 g s .28272 .35492 m .31206 .36762 L .2684 .3898 L p .713 .898 .963 r F P 0 g s .2684 .3898 m .23834 .37763 L .28272 .35492 L p .713 .898 .963 r F P 0 g s .39603 .152 m .42289 .17547 L .37883 .19083 L p .647 .803 .958 r F P 0 g s .37883 .19083 m .35141 .16785 L .39603 .152 L p .647 .803 .958 r F P 0 g s .56349 .31266 m .58741 .3319 L .54176 .34034 L p .542 .796 .992 r F P 0 g s .54176 .34034 m .51725 .32145 L .56349 .31266 L p .542 .796 .992 r F P 0 g s .51332 .15204 m .53815 .17824 L .49301 .18828 L p .586 .757 .96 r F P 0 g s .49301 .18828 m .46767 .16253 L .51332 .15204 L p .586 .757 .96 r F P 0 g s .44582 .31655 m .47193 .33289 L .42739 .34691 L p .613 .85 .988 r F P 0 g s .42739 .34691 m .40064 .33099 L .44582 .31655 L p .613 .85 .988 r F P 0 g s .75286 .34526 m .77376 .36965 L .72551 .3692 L p .447 .695 .972 r F P 0 g s .72551 .3692 m .70408 .34513 L .75286 .34526 L p .447 .695 .972 r F P 0 g s .77417 .22505 m .79533 .25837 L .74648 .25664 L p .476 .635 .924 r F P 0 g s .74648 .25664 m .72492 .22377 L .77417 .22505 L p .476 .635 .924 r F P 0 g s .70288 .19269 m .72492 .22377 L .67717 .22523 L p .498 .67 .94 r F P 0 g s .67717 .22523 m .6547 .19459 L .70288 .19269 L p .498 .67 .94 r F P 0 g s .07214 .45379 m .10616 .4616 L .06202 .49501 L p .81 .917 .911 r F P 0 g s .06202 .49501 m .02714 .48794 L .07214 .45379 L p .81 .917 .911 r F P 0 g s .68207 .32312 m .70408 .34513 L .6567 .34782 L p .47 .735 .985 r F P 0 g s .6567 .34782 m .63412 .32614 L .68207 .32312 L p .47 .735 .985 r F P 0 g s .32746 .33483 m .3561 .34802 L .31206 .36762 L p .679 .892 .975 r F P 0 g s .31206 .36762 m .28272 .35492 L .32746 .33483 L p .679 .892 .975 r F P 0 g s .63162 .16573 m .6547 .19459 L .60786 .19913 L p .523 .706 .954 r F P 0 g s .60786 .19913 m .5843 .1707 L .63162 .16573 L p .523 .706 .954 r F P 0 g s .11699 .42244 m .15019 .43093 L .10616 .4616 L p .789 .921 .926 r F P 0 g s .10616 .4616 m .07214 .45379 L .11699 .42244 L p .789 .921 .926 r F P 0 g s .44137 .13859 m .46767 .16253 L .42289 .17547 L p .614 .792 .967 r F P 0 g s .42289 .17547 m .39603 .152 L .44137 .13859 L p .614 .792 .967 r F P 0 g s .49178 .30473 m .51725 .32145 L .47193 .33289 L p .569 .834 .995 r F P 0 g s .47193 .33289 m .44582 .31655 L .49178 .30473 L p .569 .834 .995 r F P 0 g s .16182 .39382 m .1942 .40295 L .15019 .43093 L p .765 .922 .94 r F P 0 g s .15019 .43093 m .11699 .42244 L .16182 .39382 L p .765 .922 .94 r F P 0 g s .6108 .30656 m .63412 .32614 L .58741 .3319 L p .494 .775 .994 r F P 0 g s .58741 .3319 m .56349 .31266 L .6108 .30656 L p .494 .775 .994 r F P 0 g s .55999 .14406 m .5843 .1707 L .53815 .17824 L p .55 .742 .966 r F P 0 g s .53815 .17824 m .51332 .15204 L .55999 .14406 L p .55 .742 .966 r F P 0 g s .3727 .31734 m .40064 .33099 L .3561 .34802 L p .64 .882 .985 r F P 0 g s .3561 .34802 m .32746 .33483 L .3727 .31734 L p .64 .882 .985 r F P 0 g s .80322 .34833 m .82357 .37302 L .77376 .36965 L p .401 .669 .969 r F P 0 g s .77376 .36965 m .75286 .34526 L .80322 .34833 L p .401 .669 .969 r F P 0 g s .20674 .36789 m .23834 .37763 L .1942 .40295 L p .737 .922 .954 r F P 0 g s .1942 .40295 m .16182 .39382 L .20674 .36789 L p .737 .922 .954 r F P 0 g s .75259 .19354 m .77417 .22505 L .72492 .22377 L p .462 .65 .941 r F P 0 g s .72492 .22377 m .70288 .19269 L .75259 .19354 L p .462 .65 .941 r F P 0 g s .73143 .32295 m .75286 .34526 L .70408 .34513 L p .421 .709 .983 r F P 0 g s .70408 .34513 m .68207 .32312 L .73143 .32295 L p .421 .709 .983 r F P 0 g s .48758 .12765 m .51332 .15204 L .46767 .16253 L p .578 .778 .974 r F P 0 g s .46767 .16253 m .44137 .13859 L .48758 .12765 L p .578 .778 .974 r F P 0 g s .6803 .1634 m .70288 .19269 L .6547 .19459 L p .486 .687 .956 r F P 0 g s .6547 .19459 m .63162 .16573 L .6803 .1634 L p .486 .687 .956 r F P 0 g s .53867 .29558 m .56349 .31266 L .51725 .32145 L p .52 .814 .999 r F P 0 g s .51725 .32145 m .49178 .30473 L .53867 .29558 L p .52 .814 .999 r F P 0 g s .25189 .34463 m .28272 .35492 L .23834 .37763 L p .704 .918 .967 r F P 0 g s .23834 .37763 m .20674 .36789 L .25189 .34463 L p .704 .918 .967 r F P 0 g s .41857 .30247 m .44582 .31655 L .40064 .33099 L p .596 .869 .993 r F P 0 g s .40064 .33099 m .3727 .31734 L .41857 .30247 L p .596 .869 .993 r F P 0 g s .65937 .30323 m .68207 .32312 L .63412 .32614 L p .444 .75 .993 r F P 0 g s .63412 .32614 m .6108 .30656 L .65937 .30323 L p .444 .75 .993 r F P 0 g s .60784 .13866 m .63162 .16573 L .5843 .1707 L p .511 .724 .969 r F P 0 g s .5843 .1707 m .55999 .14406 L .60784 .13866 L p .511 .724 .969 r F P 0 g s .29739 .32402 m .32746 .33483 L .28272 .35492 L p .665 .911 .978 r F P 0 g s .28272 .35492 m .25189 .34463 L .29739 .32402 L p .665 .911 .978 r F P 0 g s .53482 .11924 m .55999 .14406 L .51332 .15204 L p .539 .762 .979 r F P 0 g s .51332 .15204 m .48758 .12765 L .53482 .11924 L p .539 .762 .979 r F P 0 g s .46523 .29026 m .49178 .30473 L .44582 .31655 L p .547 .851 .998 r F P 0 g s .44582 .31655 m .41857 .30247 L .46523 .29026 L p .547 .851 .998 r F P 0 g s .58665 .28915 m .6108 .30656 L .56349 .31266 L p .468 .79 .999 r F P 0 g s .56349 .31266 m .53867 .29558 L .58665 .28915 L p .468 .79 .999 r F P 0 g s .78241 .32575 m .80322 .34833 L .75286 .34526 L p .371 .681 .978 r F P 0 g s .75286 .34526 m .73143 .32295 L .78241 .32575 L p .371 .681 .978 r F P 0 g s .73052 .16383 m .75259 .19354 L .70288 .19269 L p .447 .666 .956 r F P 0 g s .70288 .19269 m .6803 .1634 L .73052 .16383 L p .447 .666 .956 r F P 0 g s .34339 .30605 m .3727 .31734 L .32746 .33483 L p .622 .9 .986 r F P 0 g s .32746 .33483 m .29739 .32402 L .34339 .30605 L p .622 .9 .986 r F P 0 g s .70938 .30278 m .73143 .32295 L .68207 .32312 L p .39 .721 .989 r F P 0 g s .68207 .32312 m .65937 .30323 L .70938 .30278 L p .39 .721 .989 r F P 0 g s .65706 .13592 m .6803 .1634 L .63162 .16573 L p .471 .704 .97 r F P 0 g s .63162 .16573 m .60784 .13866 L .65706 .13592 L p .471 .704 .97 r F P 0 g s .51282 .28075 m .53867 .29558 L .49178 .30473 L p .493 .828 .999 r F P 0 g s .49178 .30473 m .46523 .29026 L .51282 .28075 L p .493 .828 .999 r F P 0 g s .58326 .1134 m .60784 .13866 L .55999 .14406 L p .497 .742 .982 r F P 0 g s .55999 .14406 m .53482 .11924 L .58326 .1134 L p .497 .742 .982 r F P 0 g s .39002 .29075 m .41857 .30247 L .3727 .31734 L p .573 .883 .991 r F P 0 g s .3727 .31734 m .34339 .30605 L .39002 .29075 L p .573 .883 .991 r F P 0 g s .6359 .28553 m .65937 .30323 L .6108 .30656 L p .412 .761 .995 r F P 0 g s .6108 .30656 m .58665 .28915 L .6359 .28553 L p .412 .761 .995 r F P 0 g s .76103 .30533 m .78241 .32575 L .73143 .32295 L p .336 .689 .981 r F P 0 g s .73143 .32295 m .70938 .30278 L .76103 .30533 L p .336 .689 .981 r F P 0 g s .70785 .13594 m .73052 .16383 L .6803 .1634 L p .428 .681 .969 r F P 0 g s .6803 .1634 m .65706 .13592 L .70785 .13594 L p .428 .681 .969 r F P 0 g s .56153 .274 m .58665 .28915 L .53867 .29558 L p .435 .8 .995 r F P 0 g s .53867 .29558 m .51282 .28075 L .56153 .274 L p .435 .8 .995 r F P 0 g s .43744 .27814 m .46523 .29026 L .41857 .30247 L p .519 .862 .993 r F P 0 g s .41857 .30247 m .39002 .29075 L .43744 .27814 L p .519 .862 .993 r F P 0 g s .63308 .11025 m .65706 .13592 L .60784 .13866 L p .453 .72 .982 r F P 0 g s .60784 .13866 m .58326 .1134 L .63308 .11025 L p .453 .72 .982 r F P 0 g s .68661 .28482 m .70938 .30278 L .65937 .30323 L p .354 .729 .987 r F P 0 g s .65937 .30323 m .6359 .28553 L .68661 .28482 L p .354 .729 .987 r F P 0 g s .48581 .26827 m .51282 .28075 L .46523 .29026 L p .46 .835 .99 r F P 0 g s .46523 .29026 m .43744 .27814 L .48581 .26827 L p .46 .835 .99 r F P 0 g s .61152 .27009 m .6359 .28553 L .58665 .28915 L p .375 .767 .988 r F P 0 g s .58665 .28915 m .56153 .274 L .61152 .27009 L p .375 .767 .988 r F P 0 g s .6845 .10987 m .70785 .13594 L .65706 .13592 L p .407 .695 .979 r F P 0 g s .65706 .13592 m .63308 .11025 L .6845 .10987 L p .407 .695 .979 r F P 0 g s .73901 .28714 m .76103 .30533 L .70938 .30278 L p .295 .693 .975 r F P 0 g s .70938 .30278 m .68661 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RowBox[{ RowBox[{ FormBox[ SubscriptBox["f", "y"], TraditionalForm], "(", RowBox[{"x", ",", "y"}], ")"}], " ", "=", " ", RowBox[{ RowBox[{ RowBox[{"2", " ", "y"}], " ", "+", "1"}], " ", "=", " ", "0"}]}], TraditionalForm]]], ", \npor tanto ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"x", " ", "=", " ", "0"}], ";", " ", RowBox[{"y", " ", "=", " ", RowBox[{ RowBox[{"-", "1"}], "/", "2"}]}]}], TraditionalForm]]], ";\n ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"f", "(", RowBox[{"0", ",", " ", RowBox[{ RowBox[{"-", "1"}], "/", "2"}]}], ")"}], " ", "=", RowBox[{ RowBox[{"-", "5"}], "/", "4"}], " "}], TraditionalForm]]], "\nLa frontera en S es la circunferencia ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ SuperscriptBox["x", "2"], " ", "+", SuperscriptBox["y", "2"]}], "=", "1"}], TraditionalForm]]], ".\nSi ", Cell[BoxData[ FormBox["x", TraditionalForm]]], " e ", Cell[BoxData[ FormBox["y", TraditionalForm]]], " est\[AAcute]n en esta circunferencia ", Cell[BoxData[ FormBox["x", TraditionalForm]]], " e ", Cell[BoxData[ FormBox["y", TraditionalForm]]], " estar\[AAcute]n en [-1,1] .\nSustituyendo ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ SuperscriptBox["x", "2"], " ", "+", SuperscriptBox["y", "2"]}], "=", "1"}], TraditionalForm]]], " en ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"f", "(", RowBox[{"x", ",", "y"}], ")"}], " ", "=", " ", RowBox[{ SuperscriptBox["x", "2"], " ", "+", SuperscriptBox["y", "2"], "+", " ", "y", " ", "-", " ", "1"}]}], TraditionalForm]]], " \n=>", Cell[BoxData[ FormBox[ RowBox[{" ", RowBox[{ RowBox[{"g", "(", "y", ")"}], " ", "=", " ", RowBox[{ RowBox[{"1", " ", "+", " ", "y", " ", "-", " ", "1"}], "=", " ", "y"}]}]}], TraditionalForm]]], ", como y \[Element] [-1,1] g(y) es m\[AAcute]ximo para ", Cell[BoxData[ FormBox[ RowBox[{"(", RowBox[{ RowBox[{"y", " ", "=", " ", "1"}], ",", " ", RowBox[{"x", " ", "=", "0"}]}], " ", ")"}], TraditionalForm]]], "y el m\[IAcute]nimo para ", Cell[BoxData[ FormBox[ RowBox[{"(", RowBox[{ RowBox[{"y", " ", "=", " ", RowBox[{"-", "1"}]}], ",", " ", RowBox[{"x", " ", "=", "0"}]}], ")"}], TraditionalForm]]], " que unido al punto (0, -1/2) antes hallado forman los tres candidades a \ puntos optimos. A saber = (0, 1), (0,-1) y (0, -1/2) para los que obtenemos \ los siguientes valores:\n", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"f", "(", RowBox[{"0", ",", " ", "1"}], ")"}], " ", "=", "1"}], TraditionalForm]]], " m\[AAcute]ximo\n", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"f", "(", RowBox[{"0", ",", " ", RowBox[{"-", "1"}]}], ")"}], " ", "=", RowBox[{"-", "1"}]}], TraditionalForm]]], "\n", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"f", "(", RowBox[{"0", ",", " ", RowBox[{ RowBox[{"-", "1"}], "/", "2"}]}], ")"}], " ", "=", RowBox[{ RowBox[{"-", "5"}], "/", "4"}], " "}], TraditionalForm]]], " m\[IAcute]nimo" }], "Text", FontSize->16] }, Open ]], Cell[CellGroupData[{ Cell["Ejemplo 3", "Subsection"], Cell["\<\ Calcular el \[OAcute]ptimos de la funci\[OAcute]n \ \>", "Text", FontSize->16], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"z", "(", RowBox[{"x", ",", "y"}], ")"}], "=", RowBox[{ RowBox[{"2", " ", SuperscriptBox["x", "2"]}], "+", RowBox[{"6", " ", "y", " ", "x"}], "-", RowBox[{"8", " ", "x"}], "+", RowBox[{"10", " ", SuperscriptBox["y", "2"]}], "-", RowBox[{"24", " ", "y"}], "+", "16"}]}], TraditionalForm]], "Text", FontSize->16], Cell[TextData[{ "Con la condici\[OAcute]n ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"3", " ", "x"}], " ", "+", " ", RowBox[{"4", " ", "y"}]}], TraditionalForm]]], " = 6 " }], "Text", FontSize->16], Cell[CellGroupData[{ Cell["\<\ Sol.: M\[EAcute]todo de los multiplicadores de Lagrange\ \>", "Subsubsection"], Cell[TextData[{ "La condicion podemos reescribirla: ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"\[CurlyPhi]", "(", RowBox[{"x", ",", "y"}], ")"}], "=", RowBox[{ RowBox[{"3", " ", "x"}], "+", RowBox[{"4", " ", "y"}], "-", "6"}]}], TraditionalForm]]] }], "Text", FontSize->16], Cell[BoxData[ RowBox[{ RowBox[{"w", RowBox[{"(", RowBox[{"x", ",", "y"}], ")"}]}], "=", RowBox[{ RowBox[{ RowBox[{"z", RowBox[{"(", RowBox[{"x", ",", "y"}], ")"}]}], "+", RowBox[{"\[Lambda]", "\[CurlyPhi]", RowBox[{"(", RowBox[{"x", ",", "y"}], ")"}]}]}], "=", 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.81114 L s .39787 .81114 m .40529 .59895 L s .40529 .59895 m .03716 .25514 L s .68874 0 m .96935 .42924 L s .96935 .42924 m 1 .6535 L s 1 .6535 m .70298 .24544 L s .70298 .24544 m .68874 0 L s .03716 .25514 m 0 .48963 L s 0 .48963 m .70298 .24544 L s .70298 .24544 m .68874 0 L s .68874 0 m .03716 .25514 L s .40529 .59895 m .96935 .42924 L s .96935 .42924 m 1 .6535 L s 1 .6535 m .39787 .81114 L s .39787 .81114 m .40529 .59895 L s 0 0 m 1 0 L 1 .81114 L 0 .81114 L closepath clip newpath .5 Mabswid .697 .857 .959 r .38001 .65801 .40286 .66852 .44042 .653 .41804 .64219 Metetra .697 .857 .959 r .41804 .64219 .44042 .653 .47841 .63731 .45651 .62619 Metetra .697 .857 .959 r .45651 .62619 .47841 .63731 .51683 .62144 .49541 .61 Metetra .697 .857 .959 r .49541 .61 .51683 .62144 .55568 .60539 .53477 .59363 Metetra .697 .857 .959 r .53477 .59363 .55568 .60539 .59498 .58916 .57458 .57706 Metetra .697 .857 .959 r .57458 .57706 .59498 .58916 .63474 .57274 .61486 .5603 Metetra .697 .857 .959 r .61486 .5603 .63474 .57274 .67495 .55613 .65562 .54335 Metetra .697 .857 .959 r .65562 .54335 .67495 .55613 .71563 .53932 .69685 .52619 Metetra .697 .857 .959 r .69685 .52619 .71563 .53932 .75679 .52232 .73858 .50883 Metetra .697 .857 .959 r .73858 .50883 .75679 .52232 .79843 .50512 .78081 .49126 Metetra .697 .857 .959 r .78081 .49126 .79843 .50512 .84057 .48772 .82354 .47348 Metetra .697 .857 .959 r .82354 .47348 .84057 .48772 .88321 .4701 .8668 .45549 Metetra .697 .857 .959 r .8668 .45549 .88321 .4701 .92636 .45228 .91058 .43727 Metetra .697 .857 .959 r .91058 .43727 .92636 .45228 .97003 .43424 .9549 .41883 Metetra .697 .857 .959 r .35644 .64717 .38001 .65801 .41804 .64219 .39494 .63103 Metetra .697 .857 .959 r .39494 .63103 .41804 .64219 .45651 .62619 .43389 .6147 Metetra .697 .857 .959 r .43389 .6147 .45651 .62619 .49541 .61 .4733 .59819 Metetra .697 .857 .959 r .4733 .59819 .49541 .61 .53477 .59363 .51317 .58147 Metetra .697 .857 .959 r .51317 .58147 .53477 .59363 .57458 .57706 .55351 .56457 Metetra .697 .857 .959 r .55351 .56457 .57458 .57706 .61486 .5603 .59433 .54746 Metetra .697 .857 .959 r .59433 .54746 .61486 .5603 .65562 .54335 .63564 .53014 Metetra .697 .857 .959 r .63564 .53014 .65562 .54335 .69685 .52619 .67745 .51262 Metetra .697 .857 .959 r .67745 .51262 .69685 .52619 .73858 .50883 .71976 .49488 Metetra .697 .857 .959 r .71976 .49488 .73858 .50883 .78081 .49126 .76259 .47693 Metetra .697 .857 .959 r .76259 .47693 .78081 .49126 .82354 .47348 .80594 .45876 Metetra .697 .857 .959 r .80594 .45876 .82354 .47348 .8668 .45549 .84983 .44037 Metetra .697 .857 .959 r .84983 .44037 .8668 .45549 .91058 .43727 .89426 .42174 Metetra .697 .857 .959 r .89426 .42174 .91058 .43727 .9549 .41883 .93925 .40289 Metetra .697 .857 .959 r .3321 .63597 .35644 .64717 .39494 .63103 .37109 .6195 Metetra .697 .857 .959 r .37109 .6195 .39494 .63103 .43389 .6147 .41054 .60284 Metetra .697 .857 .959 r .41054 .60284 .43389 .6147 .4733 .59819 .45046 .58598 Metetra .697 .857 .959 r .45046 .58598 .4733 .59819 .51317 .58147 .49085 .56892 Metetra .697 .857 .959 r .49085 .56892 .51317 .58147 .55351 .56457 .53173 .55165 Metetra .697 .857 .959 r .53173 .55165 .55351 .56457 .59433 .54746 .57311 .53418 Metetra .697 .857 .959 r .57311 .53418 .59433 .54746 .63564 .53014 .61499 .51649 Metetra .697 .857 .959 r .61499 .51649 .63564 .53014 .67745 .51262 .65738 .49859 Metetra .697 .857 .959 r .65738 .49859 .67745 .51262 .71976 .49488 .70029 .48046 Metetra .697 .857 .959 r .70029 .48046 .71976 .49488 .76259 .47693 .74374 .46211 Metetra .697 .857 .959 r .74374 .46211 .76259 .47693 .80594 .45876 .78773 .44353 Metetra .697 .857 .959 r .78773 .44353 .80594 .45876 .84983 .44037 .83226 .42472 Metetra .697 .857 .959 r .83226 .42472 .84983 .44037 .89426 .42174 .87737 .40567 Metetra .697 .857 .959 r .87737 .40567 .89426 .42174 .93925 .40289 .92304 .38638 Metetra .697 .857 .959 r .30696 .62441 .3321 .63597 .37109 .6195 .34645 .6076 Metetra .697 .857 .959 r .34645 .6076 .37109 .6195 .41054 .60284 .38641 .59058 Metetra .697 .857 .959 r .38641 .59058 .41054 .60284 .45046 .58598 .42685 .57337 Metetra .697 .857 .959 r .42685 .57337 .45046 .58598 .49085 .56892 .46778 .55594 Metetra .697 .857 .959 r .46778 .55594 .49085 .56892 .53173 .55165 .50922 .5383 Metetra .697 .857 .959 r .50922 .5383 .53173 .55165 .57311 .53418 .55116 .52045 Metetra .697 .857 .959 r .55116 .52045 .57311 .53418 .61499 .51649 .59363 .50237 Metetra .697 .857 .959 r .59363 .50237 .61499 .51649 .65738 .49859 .63662 .48407 Metetra .697 .857 .959 r .63662 .48407 .65738 .49859 .70029 .48046 .68015 .46553 Metetra .697 .857 .959 r .68015 .46553 .70029 .48046 .74374 .46211 .72423 .44677 Metetra .697 .857 .959 r .72423 .44677 .74374 .46211 .78773 .44353 .76887 .42776 Metetra .697 .857 .959 r .76887 .42776 .78773 .44353 .83226 .42472 .81408 .40852 Metetra .697 .857 .959 r .81408 .40852 .83226 .42472 .87737 .40567 .85987 .38902 Metetra .697 .857 .959 r .85987 .38902 .87737 .40567 .92304 .38638 .90625 .36928 Metetra .697 .857 .959 r .28098 .61245 .30696 .62441 .34645 .6076 .32097 .59529 Metetra .697 .857 .959 r .32097 .59529 .34645 .6076 .38641 .59058 .36145 .57791 Metetra .697 .857 .959 r .36145 .57791 .38641 .59058 .42685 .57337 .40243 .56032 Metetra .697 .857 .959 r .40243 .56032 .42685 .57337 .46778 .55594 .44392 .54252 Metetra .697 .857 .959 r .44392 .54252 .46778 .55594 .50922 .5383 .48592 .52449 Metetra .697 .857 .959 r .48592 .52449 .50922 .5383 .55116 .52045 .52845 .50624 Metetra .697 .857 .959 r .52845 .50624 .55116 .52045 .59363 .50237 .57151 .48775 Metetra .697 .857 .959 r .57151 .48775 .59363 .50237 .63662 .48407 .61512 .46903 Metetra .697 .857 .959 r .61512 .46903 .63662 .48407 .68015 .46553 .65929 .45008 Metetra .697 .857 .959 r .65929 .45008 .68015 .46553 .72423 .44677 .70402 .43088 Metetra .697 .857 .959 r .70402 .43088 .72423 .44677 .76887 .42776 .74933 .41143 Metetra .697 .857 .959 r .74933 .41143 .76887 .42776 .81408 .40852 .79523 .39173 Metetra .697 .857 .959 r .79523 .39173 .81408 .40852 .85987 .38902 .84173 .37177 Metetra .697 .857 .959 r .84173 .37177 .85987 .38902 .90625 .36928 .88885 .35155 Metetra .697 .857 .959 r .25411 .60009 .28098 .61245 .32097 .59529 .29462 .58255 Metetra .697 .857 .959 r .29462 .58255 .32097 .59529 .36145 .57791 .33564 .5648 Metetra .697 .857 .959 r .33564 .5648 .36145 .57791 .40243 .56032 .37717 .54682 Metetra .697 .857 .959 r .37717 .54682 .40243 .56032 .44392 .54252 .41922 .52862 Metetra .697 .857 .959 r .41922 .52862 .44392 .54252 .48592 .52449 .46181 .51019 Metetra .697 .857 .959 r .46181 .51019 .48592 .52449 .52845 .50624 .50494 .49152 Metetra .697 .857 .959 r .50494 .49152 .52845 .50624 .57151 .48775 .54862 .47261 Metetra .697 .857 .959 r .54862 .47261 .57151 .48775 .61512 .46903 .59286 .45346 Metetra .697 .857 .959 r .59286 .45346 .61512 .46903 .65929 .45008 .63768 .43406 Metetra .697 .857 .959 r .63768 .43406 .65929 .45008 .70402 .43088 .68308 .41441 Metetra .697 .857 .959 r .68308 .41441 .70402 .43088 .74933 .41143 .72908 .3945 Metetra .697 .857 .959 r .72908 .3945 .74933 .41143 .79523 .39173 .77569 .37432 Metetra .697 .857 .959 r .77569 .37432 .79523 .39173 .84173 .37177 .82293 .35388 Metetra .697 .857 .959 r .82293 .35388 .84173 .37177 .88885 .35155 .87079 .33316 Metetra .697 .857 .959 r .22631 .5873 .25411 .60009 .29462 .58255 .26735 .56938 Metetra .697 .857 .959 r .26735 .56938 .29462 .58255 .33564 .5648 .30892 .55123 Metetra .697 .857 .959 r .30892 .55123 .33564 .5648 .37717 .54682 .35101 .53285 Metetra .697 .857 .959 r .35101 .53285 .37717 .54682 .41922 .52862 .39365 .51423 Metetra .697 .857 .959 r .39365 .51423 .41922 .52862 .46181 .51019 .43683 .49538 Metetra .697 .857 .959 r .43683 .49538 .46181 .51019 .50494 .49152 .48057 .47628 Metetra .697 .857 .959 r .48057 .47628 .50494 .49152 .54862 .47261 .52489 .45693 Metetra .697 .857 .959 r .52489 .45693 .54862 .47261 .59286 .45346 .56978 .43732 Metetra .697 .857 .959 r .56978 .43732 .59286 .45346 .63768 .43406 .61527 .41746 Metetra .697 .857 .959 r .61527 .41746 .63768 .43406 .68308 .41441 .66137 .39733 Metetra .697 .857 .959 r .66137 .39733 .68308 .41441 .72908 .3945 .70808 .37694 Metetra .697 .857 .959 r .70808 .37694 .72908 .3945 .77569 .37432 .75542 .35627 Metetra .697 .857 .959 r .75542 .35627 .77569 .37432 .82293 .35388 .80341 .33531 Metetra .697 .857 .959 r .80341 .33531 .82293 .35388 .87079 .33316 .85205 .31407 Metetra .697 .857 .959 r .19752 .57406 .22631 .5873 .26735 .56938 .23912 .55573 Metetra .697 .857 .959 r .23912 .55573 .26735 .56938 .30892 .55123 .28124 .53717 Metetra .697 .857 .959 r .28124 .53717 .30892 .55123 .35101 .53285 .32392 .51837 Metetra .697 .857 .959 r .32392 .51837 .35101 .53285 .39365 .51423 .36715 .49932 Metetra .697 .857 .959 r .36715 .49932 .39365 .51423 .43683 .49538 .41094 .48003 Metetra .697 .857 .959 r .41094 .48003 .43683 .49538 .48057 .47628 .45532 .46047 Metetra .697 .857 .959 r .45532 .46047 .48057 .47628 .52489 .45693 .50028 .44066 Metetra .697 .857 .959 r .50028 .44066 .52489 .45693 .56978 .43732 .54585 .42059 Metetra .697 .857 .959 r .54585 .42059 .56978 .43732 .61527 .41746 .59203 .40024 Metetra .697 .857 .959 r .59203 .40024 .61527 .41746 .66137 .39733 .63883 .37961 Metetra .697 .857 .959 r .63883 .37961 .66137 .39733 .70808 .37694 .68628 .35871 Metetra .697 .857 .959 r .68628 .35871 .70808 .37694 .75542 .35627 .73438 .33752 Metetra .697 .857 .959 r .73438 .33752 .75542 .35627 .80341 .33531 .78314 .31603 Metetra .697 .857 .959 r .78314 .31603 .80341 .33531 .85205 .31407 .83258 .29425 Metetra .697 .857 .959 r .1677 .56034 .19752 .57406 .23912 .55573 .20986 .5416 Metetra .697 .857 .959 r .20986 .5416 .23912 .55573 .28124 .53717 .25256 .5226 Metetra .697 .857 .959 r .25256 .5226 .28124 .53717 .32392 .51837 .29582 .50336 Metetra .697 .857 .959 r .29582 .50336 .32392 .51837 .36715 .49932 .33967 .48386 Metetra .697 .857 .959 r .33967 .48386 .36715 .49932 .41094 .48003 .38409 .4641 Metetra .697 .857 .959 r .38409 .4641 .41094 .48003 .45532 .46047 .42911 .44408 Metetra .697 .857 .959 r .42911 .44408 .45532 .46047 .50028 .44066 .47475 .42378 Metetra .697 .857 .959 r .47475 .42378 .50028 .44066 .54585 .42059 .521 .40321 Metetra .697 .857 .959 r .521 .40321 .54585 .42059 .59203 .40024 .56789 .38236 Metetra .697 .857 .959 r .56789 .38236 .59203 .40024 .63883 .37961 .61543 .36121 Metetra .697 .857 .959 r .61543 .36121 .63883 .37961 .68628 .35871 .66363 .33978 Metetra .697 .857 .959 r .66363 .33978 .68628 .35871 .73438 .33752 .71251 .31804 Metetra .697 .857 .959 r .71251 .31804 .73438 .33752 .78314 .31603 .76208 .29599 Metetra .697 .857 .959 r .76208 .29599 .78314 .31603 .83258 .29425 .81235 .27363 Metetra .697 .857 .959 r .1368 .54612 .1677 .56034 .20986 .5416 .17952 .52694 Metetra .697 .857 .959 r .17952 .52694 .20986 .5416 .25256 .5226 .22281 .50749 Metetra .697 .857 .959 r .22281 .50749 .25256 .5226 .29582 .50336 .26668 .48779 Metetra .697 .857 .959 r .26668 .48779 .29582 .50336 .33967 .48386 .31115 .46782 Metetra .697 .857 .959 r .31115 .46782 .33967 .48386 .38409 .4641 .35622 .44758 Metetra .697 .857 .959 r .35622 .44758 .38409 .4641 .42911 .44408 .40191 .42706 Metetra .697 .857 .959 r .40191 .42706 .42911 .44408 .47475 .42378 .44824 .40626 Metetra .697 .857 .959 r .44824 .40626 .47475 .42378 .521 .40321 .4952 .38517 Metetra .697 .857 .959 r .4952 .38517 .521 .40321 .56789 .38236 .54282 .36378 Metetra .697 .857 .959 r .54282 .36378 .56789 .38236 .61543 .36121 .59112 .34209 Metetra .697 .857 .959 r .59112 .34209 .61543 .36121 .66363 .33978 .6401 .32009 Metetra .697 .857 .959 r .6401 .32009 .66363 .33978 .71251 .31804 .68977 .29778 Metetra .697 .857 .959 r .68977 .29778 .71251 .31804 .76208 .29599 .74017 .27515 Metetra .697 .857 .959 r .74017 .27515 .76208 .29599 .81235 .27363 .79129 .25219 Metetra .697 .857 .959 r .10473 .53137 .1368 .54612 .17952 .52694 .14804 .51173 Metetra .697 .857 .959 r .14804 .51173 .17952 .52694 .22281 .50749 .19194 .49182 Metetra .697 .857 .959 r .19194 .49182 .22281 .50749 .26668 .48779 .23644 .47163 Metetra .697 .857 .959 r .23644 .47163 .26668 .48779 .31115 .46782 .28155 .45117 Metetra .697 .857 .959 r .28155 .45117 .31115 .46782 .35622 .44758 .32728 .43042 Metetra .697 .857 .959 r .32728 .43042 .35622 .44758 .40191 .42706 .37366 .40938 Metetra .697 .857 .959 r .37366 .40938 .40191 .42706 .44824 .40626 .42069 .38805 Metetra .697 .857 .959 r .42069 .38805 .44824 .40626 .4952 .38517 .46838 .36641 Metetra .697 .857 .959 r .46838 .36641 .4952 .38517 .54282 .36378 .51676 .34446 Metetra .697 .857 .959 r .51676 .34446 .54282 .36378 .59112 .34209 .56583 .3222 Metetra .697 .857 .959 r .56583 .3222 .59112 .34209 .6401 .32009 .61561 .29962 Metetra .697 .857 .959 r .61561 .29962 .6401 .32009 .68977 .29778 .66612 .27671 Metetra .697 .857 .959 r .66612 .27671 .68977 .29778 .74017 .27515 .71737 .25346 Metetra .697 .857 .959 r .71737 .25346 .74017 .27515 .79129 .25219 .76937 .22987 Metetra .697 .857 .959 r .07145 .51606 .10473 .53137 .14804 .51173 .11536 .49594 Metetra .697 .857 .959 r .11536 .49594 .14804 .51173 .19194 .49182 .15988 .47553 Metetra .697 .857 .959 r .15988 .47553 .19194 .49182 .23644 .47163 .20501 .45484 Metetra .697 .857 .959 r .20501 .45484 .23644 .47163 .28155 .45117 .25078 .43386 Metetra .697 .857 .959 r .25078 .43386 .28155 .45117 .32728 .43042 .2972 .41258 Metetra .697 .857 .959 r .2972 .41258 .32728 .43042 .37366 .40938 .34428 .391 Metetra .697 .857 .959 r .34428 .391 .37366 .40938 .42069 .38805 .39204 .36911 Metetra .697 .857 .959 r .39204 .36911 .42069 .38805 .46838 .36641 .44048 .3469 Metetra .697 .857 .959 r .44048 .3469 .46838 .36641 .51676 .34446 .48964 .32437 Metetra .697 .857 .959 r .48964 .32437 .51676 .34446 .56583 .3222 .53951 .30151 Metetra .697 .857 .959 r .53951 .30151 .56583 .3222 .61561 .29962 .59012 .27831 Metetra .697 .857 .959 r .59012 .27831 .61561 .29962 .66612 .27671 .64148 .25476 Metetra .697 .857 .959 r .64148 .25476 .66612 .27671 .71737 .25346 .69361 .23086 Metetra .697 .857 .959 r .69361 .23086 .71737 .25346 .76937 .22987 .74654 .2066 Metetra .697 .857 .959 r .03688 .50016 .07145 .51606 .11536 .49594 .08141 .47953 Metetra .697 .857 .959 r .08141 .47953 .11536 .49594 .15988 .47553 .12656 .45861 Metetra .697 .857 .959 r .12656 .45861 .15988 .47553 .20501 .45484 .17235 .43739 Metetra .697 .857 .959 r .17235 .43739 .20501 .45484 .25078 .43386 .2188 .41586 Metetra .697 .857 .959 r .2188 .41586 .25078 .43386 .2972 .41258 .26592 .39403 Metetra .697 .857 .959 r .26592 .39403 .2972 .41258 .34428 .391 .31372 .37188 Metetra .697 .857 .959 r .31372 .37188 .34428 .391 .39204 .36911 .36222 .3494 Metetra .697 .857 .959 r .36222 .3494 .39204 .36911 .44048 .3469 .41144 .32659 Metetra .697 .857 .959 r .41144 .32659 .44048 .3469 .48964 .32437 .46139 .30344 Metetra .697 .857 .959 r .46139 .30344 .48964 .32437 .53951 .30151 .51209 .27995 Metetra .697 .857 .959 r .51209 .27995 .53951 .30151 .59012 .27831 .56356 .2561 Metetra .697 .857 .959 r .56356 .2561 .59012 .27831 .64148 .25476 .6158 .23189 Metetra .697 .857 .959 r .6158 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g s .68924 .5202 m .7073 .5324 L .66844 .54874 L p .699 .862 .96 r F P 0 g s .66844 .54874 m .64987 .53686 L .68924 .5202 L p .699 .862 .96 r F P 0 g s .43624 .66839 m .45809 .68659 L .42074 .69383 L p .607 .759 .952 r F P 0 g s .42074 .69383 m .39856 .67587 L .43624 .66839 L p .607 .759 .952 r F P 0 g s .53458 .67176 m .55518 .68996 L .51698 .69719 L p .607 .759 .952 r F P 0 g s .51698 .69719 m .49603 .67923 L .53458 .67176 L p .607 .759 .952 r F P 0 g s .45372 .57943 m .47553 .59074 L .4378 .60682 L p .699 .862 .96 r F P 0 g s .4378 .60682 m .41551 .59582 L .45372 .57943 L p .699 .862 .96 r F P 0 g s .59126 .54142 m .61094 .55334 L .57243 .56964 L p .699 .862 .96 r F P 0 g s .57243 .56964 m .55226 .55804 L .59126 .54142 L p .699 .862 .96 r F P 0 g s .72906 .50335 m .74659 .51588 L .7073 .5324 L p .699 .862 .96 r F P 0 g s .7073 .5324 m .68924 .5202 L .72906 .50335 L p .699 .862 .96 r F P 0 g s .37579 .65743 m .39856 .67587 L .36148 .68324 L p .607 .759 .952 r F P 0 g s .36148 .68324 m .33839 .66504 L .37579 .65743 L p .607 .759 .952 r F P 0 g s .47452 .66079 m .49603 .67923 L .45809 .68659 L p .607 .759 .952 r F P 0 g s .45809 .68659 m .43624 .66839 L .47452 .66079 L p .607 .759 .952 r F P 0 g s .35425 .60101 m .37773 .61204 L .34037 .62807 L p .699 .862 .96 r F P 0 g s .34037 .62807 m .31642 .61736 L .35425 .60101 L p .699 .862 .96 r F P 0 g s .49235 .56284 m .51368 .57448 L .47553 .59074 L p .699 .862 .96 r F P 0 g s .47553 .59074 m .45372 .57943 L .49235 .56284 L p .699 .862 .96 r F P 0 g s .63071 .52461 m .64987 .53686 L .61094 .55334 L p .699 .862 .96 r F P 0 g s .61094 .55334 m .59126 .54142 L .63071 .52461 L p .699 .862 .96 r F P 0 g s .57375 .66417 m .59399 .68261 L .55518 .68996 L p .607 .759 .952 r F P 0 g s .55518 .68996 m .53458 .67176 L .57375 .66417 L p .607 .759 .952 r F P 0 g s .76932 .4863 m .78631 .49918 L .74659 .51588 L p .699 .862 .96 r F P 0 g s .74659 .51588 m .72906 .50335 L .76932 .4863 L p .699 .862 .96 r F P 0 g s .41379 .6497 m .43624 .66839 L .39856 .67587 L p .607 .759 .952 r F P 0 g s .39856 .67587 m .37579 .65743 L .41379 .6497 L p .607 .759 .952 r F P 0 g s .39251 .58447 m .41551 .59582 L .37773 .61204 L p .699 .862 .96 r F P 0 g s .37773 .61204 m .35425 .60101 L .39251 .58447 L p .699 .862 .96 r F P 0 g s .53143 .54607 m .55226 .55804 L .51368 .57448 L p .699 .862 .96 r F P 0 g s .51368 .57448 m .49235 .56284 L .53143 .54607 L p .699 .862 .96 r F P 0 g s .67061 .50761 m .68924 .5202 L .64987 .53686 L p .699 .862 .96 r F P 0 g s .64987 .53686 m .63071 .52461 L .67061 .50761 L p .699 .862 .96 r F P 0 g s .51342 .65307 m .53458 .67176 L .49603 .67923 L p .607 .759 .952 r F P 0 g s .49603 .67923 m .47452 .66079 L .51342 .65307 L p .607 .759 .952 r F P 0 g s .81004 .46907 m .82648 .48228 L .78631 .49918 L p .699 .862 .96 r F P 0 g s .78631 .49918 m .76932 .4863 L .81004 .46907 L p .699 .862 .96 r F P 0 g s .61357 .65645 m .63343 .67515 L .59399 .68261 L p .607 .759 .952 r F P 0 g s .59399 .68261 m .57375 .66417 L .61357 .65645 L p .607 .759 .952 r F P 0 g s .35238 .63849 m .37579 .65743 L .33839 .66504 L p .607 .759 .952 r F P 0 g s .33839 .66504 m .31466 .64635 L .35238 .63849 L p .607 .759 .952 r F P 0 g s .4312 .56774 m .45372 .57943 L .41551 .59582 L p .699 .862 .96 r F P 0 g s .41551 .59582 m .39251 .58447 L .4312 .56774 L p .699 .862 .96 r F P 0 g s .57095 .52911 m .59126 .54142 L .55226 .55804 L p .699 .862 .96 r F P 0 g s .55226 .55804 m .53143 .54607 L .57095 .52911 L p .699 .862 .96 r F P 0 g s .71096 .49041 m .72906 .50335 L .68924 .5202 L p .699 .862 .96 r F P 0 g s .68924 .5202 m .67061 .50761 L .71096 .49041 L p .699 .862 .96 r F P 0 g s .45241 .64185 m .47452 .66079 L .43624 .66839 L p .607 .759 .952 r F P 0 g s .43624 .66839 m .41379 .6497 L .45241 .64185 L p .607 .759 .952 r F P 0 g s .85123 .45164 m .8671 .4652 L .82648 .48228 L p .699 .862 .96 r F P 0 g s .82648 .48228 m .81004 .46907 L .85123 .45164 L p .699 .862 .96 r F P 0 g s .55296 .64522 m .57375 .66417 L .53458 .67176 L p .607 .759 .952 r F P 0 g s .53458 .67176 m .51342 .65307 L .55296 .64522 L p .607 .759 .952 r F P 0 g s .33 .58962 m .35425 .60101 L .31642 .61736 L p .699 .862 .96 r F P 0 g s .31642 .61736 m .2917 .6063 L .33 .58962 L p .699 .862 .96 r F P 0 g s .47034 .55082 m .49235 .56284 L .45372 .57943 L p .699 .862 .96 r F P 0 g s .45372 .57943 m .4312 .56774 L .47034 .55082 L p .699 .862 .96 r F P 0 g s .61093 .51195 m .63071 .52461 L .59126 .54142 L p .699 .862 .96 r F P 0 g s .59126 .54142 m .57095 .52911 L .61093 .51195 L p .699 .862 .96 r F P 0 g s .65403 .64861 m .6735 .66756 L .63343 .67515 L p .607 .759 .952 r F P 0 g s .63343 .67515 m .61357 .65645 L .65403 .64861 L p .607 .759 .952 r F P 0 g s .75178 .47301 m .76932 .4863 L .72906 .50335 L p .699 .862 .96 r F P 0 g s .72906 .50335 m .71096 .49041 L .75178 .47301 L p .699 .862 .96 r F P 0 g s .39072 .6305 m .41379 .6497 L .37579 .65743 L p .607 .759 .952 r F P 0 g s .37579 .65743 m .35238 .63849 L .39072 .6305 L p .607 .759 .952 r F P 0 g s .89289 .434 m .90818 .44793 L .8671 .4652 L p .699 .862 .96 r F P 0 g s .8671 .4652 m .85123 .45164 L .89289 .434 L p .699 .862 .96 r F P 0 g s .49167 .63386 m .51342 .65307 L .47452 .66079 L p .607 .759 .952 r F P 0 g s .47452 .66079 m .45241 .64185 L .49167 .63386 L p .607 .759 .952 r F P 0 g s .36875 .57275 m .39251 .58447 L .35425 .60101 L p .699 .862 .96 r F P 0 g s .35425 .60101 m .33 .58962 L .36875 .57275 L p .699 .862 .96 r F P 0 g s .50992 .53371 m .53143 .54607 L .49235 .56284 L p .699 .862 .96 r F P 0 g s .49235 .56284 m .47034 .55082 L .50992 .53371 L p .699 .862 .96 r F P 0 g s .65136 .4946 m .67061 .50761 L .63071 .52461 L p .699 .862 .96 r F P 0 g s .63071 .52461 m .61093 .51195 L .65136 .4946 L p .699 .862 .96 r F P 0 g s .59315 .63724 m .61357 .65645 L .57375 .66417 L p .607 .759 .952 r F P 0 g s .57375 .66417 m .55296 .64522 L .59315 .63724 L p .607 .759 .952 r F P 0 g s .79307 .45542 m .81004 .46907 L .76932 .4863 L p .699 .862 .96 r F P 0 g s .76932 .4863 m .75178 .47301 L .79307 .45542 L p .699 .862 .96 r F P 0 g s .32833 .61902 m .35238 .63849 L .31466 .64635 L p .607 .759 .952 r F P 0 g s .31466 .64635 m .29029 .62715 L .32833 .61902 L p .607 .759 .952 r F P 0 g s .93503 .41616 m .94973 .43046 L .90818 .44793 L p .699 .862 .96 r F P 0 g s .90818 .44793 m .89289 .434 L .93503 .41616 L p .699 .862 .96 r F P 0 g s .69517 .64064 m .71423 .65986 L .6735 .66756 L p .607 .759 .952 r F P 0 g s .6735 .66756 m .65403 .64861 L .69517 .64064 L p .607 .759 .952 r F P 0 g s .42969 .62237 m .45241 .64185 L .41379 .6497 L p .607 .759 .952 r F P 0 g s .41379 .6497 m .39072 .6305 L .42969 .62237 L p .607 .759 .952 r F P 0 g s .40794 .55567 m .4312 .56774 L .39251 .58447 L p .699 .862 .96 r F P 0 g s .39251 .58447 m .36875 .57275 L .40794 .55567 L p .699 .862 .96 r F P 0 g s .54997 .5164 m .57095 .52911 L .53143 .54607 L p .699 .862 .96 r F P 0 g s .53143 .54607 m .50992 .53371 L .54997 .5164 L p .699 .862 .96 r F P 0 g s .69227 .47704 m .71096 .49041 L .67061 .50761 L p .699 .862 .96 r F P 0 g s .67061 .50761 m .65136 .4946 L .69227 .47704 L p .699 .862 .96 r F P 0 g s .53158 .62574 m .55296 .64522 L .51342 .65307 L p .607 .759 .952 r F P 0 g s .51342 .65307 m .49167 .63386 L .53158 .62574 L p .607 .759 .952 r F P 0 g s .83483 .43762 m .85123 .45164 L .81004 .46907 L p .699 .862 .96 r F P 0 g s .81004 .46907 m .79307 .45542 L .83483 .43762 L p .699 .862 .96 r F P 0 g s .30496 .57786 m .33 .58962 L .2917 .6063 L p .699 .862 .96 r F P 0 g s .2917 .6063 m .26617 .59488 L .30496 .57786 L p .699 .862 .96 r F P 0 g s .63402 .62913 m .65403 .64861 L .61357 .65645 L p .607 .759 .952 r F P 0 g s .61357 .65645 m .59315 .63724 L .63402 .62913 L p .607 .759 .952 r F P 0 g s .367 .61075 m .39072 .6305 L .35238 .63849 L p .607 .759 .952 r F P 0 g s .35238 .63849 m .32833 .61902 L .367 .61075 L p .607 .759 .952 r F P 0 g s .44759 .53841 m .47034 .55082 L .4312 .56774 L p .699 .862 .96 r F P 0 g s .4312 .56774 m .40794 .55567 L .44759 .53841 L p .699 .862 .96 r F P 0 g s .59049 .49888 m .61093 .51195 L .57095 .52911 L p .699 .862 .96 r F P 0 g s .57095 .52911 m .54997 .5164 L .59049 .49888 L p .699 .862 .96 r F P 0 g s .73699 .63253 m .75563 .65202 L .71423 .65986 L p .607 .759 .952 r F P 0 g s .71423 .65986 m .69517 .64064 L .73699 .63253 L p .607 .759 .952 r F P 0 g s .73365 .45928 m .75178 .47301 L .71096 .49041 L p .699 .862 .96 r F P 0 g s .71096 .49041 m .69227 .47704 L .73365 .45928 L p .699 .862 .96 r F P 0 g s .46931 .61411 m .49167 .63386 L .45241 .64185 L p .607 .759 .952 r F P 0 g s .45241 .64185 m .42969 .62237 L .46931 .61411 L p .607 .759 .952 r F P 0 g s .87709 .41961 m .89289 .434 L .85123 .45164 L p .699 .862 .96 r F P 0 g s .85123 .45164 m .83483 .43762 L .87709 .41961 L p .699 .862 .96 r F P 0 g s .57217 .61748 m .59315 .63724 L .55296 .64522 L p .607 .759 .952 r F P 0 g s .55296 .64522 m .53158 .62574 L .57217 .61748 L p .607 .759 .952 r F P 0 g s .3442 .56063 m .36875 .57275 L .33 .58962 L p .699 .862 .96 r F P 0 g s .33 .58962 m .30496 .57786 L .3442 .56063 L p .699 .862 .96 r F P 0 g s .30359 .59899 m .32833 .61902 L .29029 .62715 L p .607 .759 .952 r F P 0 g s .29029 .62715 m .26522 .60741 L .30359 .59899 L p .607 .759 .952 r F P 0 g s .4877 .52093 m .50992 .53371 L .47034 .55082 L p .699 .862 .96 r F P 0 g s .47034 .55082 m .44759 .53841 L .4877 .52093 L p .699 .862 .96 r F P 0 g s .63148 .48116 m .65136 .4946 L .61093 .51195 L p .699 .862 .96 r F P 0 g s .61093 .51195 m .59049 .49888 L .63148 .48116 L p .699 .862 .96 r F P 0 g s .67557 .62088 m .69517 .64064 L .65403 .64861 L p .607 .759 .952 r F P 0 g s .65403 .64861 m .63402 .62913 L .67557 .62088 L p .607 .759 .952 r F P 0 g s .77552 .44131 m .79307 .45542 L .75178 .47301 L p .699 .862 .96 r F P 0 g s .75178 .47301 m .73365 .45928 L .77552 .44131 L p .699 .862 .96 r F P 0 g s .40632 .60234 m .42969 .62237 L .39072 .6305 L p .607 .759 .952 r F P 0 g s .39072 .6305 m .367 .61075 L .40632 .60234 L p .607 .759 .952 r F P 0 g s .91984 .40139 m .93503 .41616 L .89289 .434 L p .699 .862 .96 r F P 0 g s .89289 .434 m .87709 .41961 L .91984 .40139 L p .699 .862 .96 r F P 0 g s .77951 .62429 m .79771 .64406 L .75563 .65202 L p .607 .759 .952 r F P 0 g s .75563 .65202 m .73699 .63253 L .77951 .62429 L p .607 .759 .952 r F P 0 g s .5096 .60571 m .53158 .62574 L .49167 .63386 L p .607 .759 .952 r F P 0 g s .49167 .63386 m .46931 .61411 L .5096 .60571 L p .607 .759 .952 r F P 0 g s .3839 .5432 m .40794 .55567 L .36875 .57275 L p .699 .862 .96 r F P 0 g s .36875 .57275 m .3442 .56063 L .3839 .5432 L p .699 .862 .96 r F P 0 g s .52829 .50326 m .54997 .5164 L .50992 .53371 L p .699 .862 .96 r F P 0 g s .50992 .53371 m .4877 .52093 L .52829 .50326 L p .699 .862 .96 r F P 0 g s .67295 .46323 m .69227 .47704 L .65136 .4946 L p .699 .862 .96 r F P 0 g s .65136 .4946 m .63148 .48116 L .67295 .46323 L p .699 .862 .96 r F P 0 g s .61343 .60909 m .63402 .62913 L .59315 .63724 L p .607 .759 .952 r F P 0 g s .59315 .63724 m .57217 .61748 L .61343 .60909 L p .607 .759 .952 r F P 0 g s .81789 .42313 m .83483 .43762 L .79307 .45542 L p .699 .862 .96 r F P 0 g s .79307 .45542 m .77552 .44131 L .81789 .42313 L p .699 .862 .96 r F P 0 g s .34261 .59044 m .367 .61075 L .32833 .61902 L p .607 .759 .952 r F P 0 g s .32833 .61902 m .30359 .59899 L .34261 .59044 L p .607 .759 .952 r F P 0 g s .27907 .56569 m .30496 .57786 L .26617 .59488 L p .699 .862 .96 r F P 0 g s .26617 .59488 m .23979 .58308 L .27907 .56569 L p .699 .862 .96 r F P 0 g s .71782 .61249 m .73699 .63253 L .69517 .64064 L p .607 .759 .952 r F P 0 g s .69517 .64064 m .67557 .62088 L .71782 .61249 L p .607 .759 .952 r F P 0 g s .44631 .59379 m .46931 .61411 L .42969 .62237 L p .607 .759 .952 r F P 0 g s .42969 .62237 m .40632 .60234 L .44631 .59379 L p .607 .759 .952 r F P 0 g s .42407 .52557 m .44759 .53841 L .40794 .55567 L p .699 .862 .96 r F P 0 g s .40794 .55567 m .3839 .5432 L .42407 .52557 L p .699 .862 .96 r F P 0 g s .56936 .48537 m .59049 .49888 L .54997 .5164 L p .699 .862 .96 r F P 0 g s .54997 .5164 m .52829 .50326 L .56936 .48537 L p .699 .862 .96 r F P 0 g s .82276 .61591 m .8405 .63596 L .79771 .64406 L p .607 .759 .952 r F P 0 g s .79771 .64406 m .77951 .62429 L .82276 .61591 L p .607 .759 .952 r F P 0 g s .71492 .44509 m .73365 .45928 L .69227 .47704 L p .699 .862 .96 r F P 0 g s .69227 .47704 m .67295 .46323 L .71492 .44509 L p .699 .862 .96 r F P 0 g s .55058 .59716 m .57217 .61748 L .53158 .62574 L p .607 .759 .952 r F P 0 g s .53158 .62574 m .5096 .60571 L .55058 .59716 L p .607 .759 .952 r F P 0 g s .27815 .5784 m .30359 .59899 L .26522 .60741 L p .607 .759 .952 r F P 0 g s .26522 .60741 m .23945 .5871 L .27815 .5784 L p .607 .759 .952 r F P 0 g s .86076 .40473 m .87709 .41961 L .83483 .43762 L p .699 .862 .96 r F P 0 g s .83483 .43762 m .81789 .42313 L .86076 .40473 L p .699 .862 .96 r F P 0 g s .31882 .54811 m .3442 .56063 L .30496 .57786 L p .699 .862 .96 r F P 0 g s .30496 .57786 m .27907 .56569 L .31882 .54811 L p .699 .862 .96 r F P 0 g s .6554 .60055 m .67557 .62088 L .63402 .62913 L p .607 .759 .952 r F P 0 g s .63402 .62913 m .61343 .60909 L .6554 .60055 L p .607 .759 .952 r F P 0 g s .38229 .58174 m .40632 .60234 L .367 .61075 L p .607 .759 .952 r F P 0 g s .367 .61075 m .34261 .59044 L .38229 .58174 L p .607 .759 .952 r F P 0 g s .46473 .50773 m .4877 .52093 L .44759 .53841 L p .699 .862 .96 r F P 0 g s .44759 .53841 m .42407 .52557 L .46473 .50773 L p .699 .862 .96 r F P 0 g s .61091 .46727 m .63148 .48116 L .59049 .49888 L p .699 .862 .96 r F P 0 g s .59049 .49888 m .56936 .48537 L .61091 .46727 L p .699 .862 .96 r F P 0 g s .76079 .60396 m .77951 .62429 L .73699 .63253 L p .607 .759 .952 r F P 0 g s .73699 .63253 m .71782 .61249 L .76079 .60396 L p .607 .759 .952 r F P 0 g s .75738 .42673 m .77552 .44131 L .73365 .45928 L p .699 .862 .96 r F P 0 g s .73365 .45928 m .71492 .44509 L .75738 .42673 L p .699 .862 .96 r F P 0 g s .48699 .5851 m .5096 .60571 L .46931 .61411 L p .607 .759 .952 r F P 0 g s .46931 .61411 m .44631 .59379 L .48699 .5851 L p .607 .759 .952 r F P 0 g s .90414 .38611 m .91984 .40139 L .87709 .41961 L p .699 .862 .96 r F P 0 g s .87709 .41961 m .86076 .40473 L .90414 .38611 L p .699 .862 .96 r F P 0 g s .86675 .60738 m .88402 .62772 L .8405 .63596 L p .607 .759 .952 r F P 0 g s .8405 .63596 m .82276 .61591 L .86675 .60738 L p .607 .759 .952 r F P 0 g s .59225 .58847 m .61343 .60909 L .57217 .61748 L p .607 .759 .952 r F P 0 g s .57217 .61748 m .55058 .59716 L .59225 .58847 L p .607 .759 .952 r F P 0 g s .35904 .53031 m .3839 .5432 L .3442 .56063 L p .699 .862 .96 r F P 0 g s .3442 .56063 m .31882 .54811 L .35904 .53031 L p .699 .862 .96 r F P 0 g s .31751 .56954 m .34261 .59044 L .30359 .59899 L p .607 .759 .952 r F P 0 g s .30359 .59899 m .27815 .5784 L .31751 .56954 L p .607 .759 .952 r F P 0 g s .50587 .48967 m .52829 .50326 L .4877 .52093 L p .699 .862 .96 r F P 0 g s .4877 .52093 m .46473 .50773 L .50587 .48967 L p .699 .862 .96 r F P 0 g s .65297 .44895 m .67295 .46323 L .63148 .48116 L p .699 .862 .96 r F P 0 g s .63148 .48116 m .61091 .46727 L .65297 .44895 L p .699 .862 .96 r F P 0 g s .69809 .59187 m .71782 .61249 L .67557 .62088 L p .607 .759 .952 r F P 0 g s .67557 .62088 m .6554 .60055 L .69809 .59187 L p .607 .759 .952 r F P 0 g s .80036 .40815 m .81789 .42313 L .77552 .44131 L p .699 .862 .96 r F P 0 g s .77552 .44131 m .75738 .42673 L .80036 .40815 L p .699 .862 .96 r F P 0 g s .42265 .57289 m .44631 .59379 L .40632 .60234 L p .607 .759 .952 r F P 0 g s .40632 .60234 m .38229 .58174 L .42265 .57289 L p .607 .759 .952 r F P 0 g s .2523 .55312 m .27907 .56569 L .23979 .58308 L p .699 .862 .96 r F P 0 g s .23979 .58308 m .22717 .57743 L p .2523 .55312 L .699 .862 .96 r F P 0 g s .23945 .5871 m .22717 .57743 L p .25197 .5572 L .607 .759 .952 r F P 0 g s .22717 .57743 m .21294 .56622 L .23367 .56143 L p .607 .759 .952 r F P 0 g s .23367 .56143 m .2523 .55312 L p .22717 .57743 L .699 .862 .96 r F P 0 g s .23367 .56143 m .25197 .5572 L p .22717 .57743 L .607 .759 .952 r F P 0 g s .22717 .57743 m .21251 .57087 L .23367 .56143 L p .699 .862 .96 r F P 0 g s .80451 .59528 m .82276 .61591 L .77951 .62429 L p .607 .759 .952 r F P 0 g s .77951 .62429 m .76079 .60396 L .80451 .59528 L p .607 .759 .952 r F P 0 g s .52836 .57625 m .55058 .59716 L .5096 .60571 L p .607 .759 .952 r F P 0 g s .5096 .60571 m .48699 .5851 L .52836 .57625 L p .607 .759 .952 r F P 0 g s .39976 .5123 m .42407 .52557 L .3839 .5432 L p .699 .862 .96 r F P 0 g s .3839 .5432 m .35904 .53031 L .39976 .5123 L p .699 .862 .96 r F P 0 g s .25197 .5572 m .27815 .5784 L .23945 .5871 L p .607 .759 .952 r F P 0 g s .5475 .47139 m .56936 .48537 L .52829 .50326 L p .699 .862 .96 r F P 0 g s .52829 .50326 m .50587 .48967 L .5475 .47139 L p .699 .862 .96 r F P 0 g s .69554 .43041 m .71492 .44509 L .67295 .46323 L p .699 .862 .96 r F P 0 g s .67295 .46323 m .65297 .44895 L .69554 .43041 L p .699 .862 .96 r F P 0 g s .9115 .59871 m .92827 .61935 L .88402 .62772 L p .607 .759 .952 r F P 0 g s .88402 .62772 m .86675 .60738 L .9115 .59871 L p .607 .759 .952 r F P 0 g s .63465 .57963 m .6554 .60055 L .61343 .60909 L p .607 .759 .952 r F P 0 g s .61343 .60909 m .59225 .58847 L .63465 .57963 L p .607 .759 .952 r F P 0 g s .84386 .38935 m .86076 .40473 L .81789 .42313 L p .699 .862 .96 r F P 0 g s .81789 .42313 m .80036 .40815 L .84386 .38935 L p .699 .862 .96 r F P 0 g s .35755 .56053 m .38229 .58174 L .34261 .59044 L p .607 .759 .952 r F P 0 g s .34261 .59044 m .31751 .56954 L .35755 .56053 L p .607 .759 .952 r F P 0 g s .29257 .53515 m .31882 .54811 L .27907 .56569 L p .699 .862 .96 r F P 0 g s .27907 .56569 m .2523 .55312 L .29257 .53515 L p .699 .862 .96 r F P 0 g s .74152 .58303 m .76079 .60396 L .71782 .61249 L p .607 .759 .952 r F P 0 g s .71782 .61249 m .69809 .59187 L .74152 .58303 L p .607 .759 .952 r F P 0 g s .46371 .56388 m .48699 .5851 L .44631 .59379 L p .607 .759 .952 r F P 0 g s .44631 .59379 m .42265 .57289 L .46371 .56388 L p .607 .759 .952 r F P 0 g s .44096 .49406 m .46473 .50773 L .42407 .52557 L p .699 .862 .96 r F P 0 g s .42407 .52557 m .39976 .5123 L .44096 .49406 L p .699 .862 .96 r F P 0 g s .58964 .45289 m .61091 .46727 L .56936 .48537 L p .699 .862 .96 r F P 0 g s .56936 .48537 m .5475 .47139 L .58964 .45289 L p .699 .862 .96 r F P 0 g s .84898 .58645 m .86675 .60738 L .82276 .61591 L p .607 .759 .952 r F P 0 g s .82276 .61591 m .80451 .59528 L .84898 .58645 L p .607 .759 .952 r F P 0 g s .73862 .41164 m .75738 .42673 L .71492 .44509 L p .699 .862 .96 r F P 0 g s .71492 .44509 m .69554 .43041 L .73862 .41164 L p .699 .862 .96 r F P 0 g s .57046 .56725 m .59225 .58847 L .55058 .59716 L p .607 .759 .952 r F P 0 g s .55058 .59716 m .52836 .57625 L .57046 .56725 L p .607 .759 .952 r F P 0 g s .29168 .54804 m .31751 .56954 L .27815 .5784 L p .607 .759 .952 r F P 0 g s .27815 .5784 m .25197 .5572 L .29168 .54804 L p .607 .759 .952 r F P 0 g s .88789 .37031 m .90414 .38611 L .86076 .40473 L p .699 .862 .96 r F P 0 g s .86076 .40473 m .84386 .38935 L .88789 .37031 L p .699 .862 .96 r F P 0 g s .95703 .58988 m .97329 .61083 L .92827 .61935 L p .607 .759 .952 r F P 0 g s .92827 .61935 m .9115 .59871 L .95703 .58988 L p .607 .759 .952 r F P 0 g s .33333 .51697 m .35904 .53031 L .31882 .54811 L p .699 .862 .96 r F P 0 g s .31882 .54811 m .29257 .53515 L .33333 .51697 L p .699 .862 .96 r F P 0 g s .67779 .57064 m .69809 .59187 L .6554 .60055 L p .607 .759 .952 r F P 0 g s .6554 .60055 m .63465 .57963 L .67779 .57064 L p .607 .759 .952 r F P 0 g s .39829 .55137 m .42265 .57289 L .38229 .58174 L p .607 .759 .952 r F P 0 g s .38229 .58174 m .35755 .56053 L .39829 .55137 L p .607 .759 .952 r F P 0 g s .48267 .47561 m .50587 .48967 L .46473 .50773 L p .699 .862 .96 r F P 0 g s .46473 .50773 m .44096 .49406 L .48267 .47561 L p .699 .862 .96 r F P 0 g s .6323 .43417 m .65297 .44895 L .61091 .46727 L p .699 .862 .96 r F P 0 g s .61091 .46727 m .58964 .45289 L .6323 .43417 L p .699 .862 .96 r F P 0 g s .78571 .57404 m .80451 .59528 L .76079 .60396 L p .607 .759 .952 r F P 0 g s .76079 .60396 m .74152 .58303 L .78571 .57404 L p .607 .759 .952 r F P 0 g s .78223 .39265 m .80036 .40815 L .75738 .42673 L p .699 .862 .96 r F P 0 g s .75738 .42673 m .73862 .41164 L .78223 .39265 L p .699 .862 .96 r F P 0 g s .50549 .55472 m .52836 .57625 L .48699 .5851 L p .607 .759 .952 r F P 0 g s .48699 .5851 m .46371 .56388 L .50549 .55472 L p .607 .759 .952 r F P 0 g s .22501 .53539 m .23949 .5471 L p .21294 .56622 L .607 .759 .952 r F P 0 g s .23367 .56143 m .21294 .56622 L p .23949 .5471 L .607 .759 .952 r F P 0 g s .22459 .54011 m .23949 .5471 L p .21251 .57087 L .699 .862 .96 r F P 0 g s .23949 .5471 m .2523 .55312 L .23367 .56143 L p .699 .862 .96 r F P 0 g s .23367 .56143 m .21251 .57087 L p .23949 .5471 L .699 .862 .96 r F P 0 g s .23949 .5471 m .25197 .5572 L .23367 .56143 L p .607 .759 .952 r F P 0 g s .21294 .56622 m .18565 .54472 L .22501 .53539 L p .607 .759 .952 r F P 0 g s .21251 .57087 m .18428 .55824 L .22459 .54011 L p .699 .862 .96 r F P 0 g s .89424 .57746 m .9115 .59871 L .86675 .60738 L p .607 .759 .952 r F P 0 g s .86675 .60738 m .84898 .58645 L .89424 .57746 L p .607 .759 .952 r F P 0 g s .61329 .55809 m .63465 .57963 L .59225 .58847 L p .607 .759 .952 r F P 0 g s .59225 .58847 m .57046 .56725 L .61329 .55809 L p .607 .759 .952 r F P 0 g s .37459 .49856 m .39976 .5123 L .35904 .53031 L p .699 .862 .96 r F P 0 g s .35904 .53031 m .33333 .51697 L .37459 .49856 L p .699 .862 .96 r F P 0 g s .33208 .5387 m .35755 .56053 L .31751 .56954 L p .607 .759 .952 r F P 0 g s .31751 .56954 m .29168 .54804 L .33208 .5387 L p .607 .759 .952 r F P 0 g s .52489 .45693 m .5475 .47139 L .50587 .48967 L p .699 .862 .96 r F P 0 g s .50587 .48967 m .48267 .47561 L .52489 .45693 L p .699 .862 .96 r F P 0 g s .67548 .41522 m .69554 .43041 L .65297 .44895 L p .699 .862 .96 r F P 0 g s .65297 .44895 m .6323 .43417 L .67548 .41522 L p .699 .862 .96 r F P 0 g s .72168 .56148 m .74152 .58303 L .69809 .59187 L p .607 .759 .952 r F P 0 g s .69809 .59187 m .67779 .57064 L .72168 .56148 L p .607 .759 .952 r F P 0 g s .82638 .37342 m .84386 .38935 L .80036 .40815 L p .699 .862 .96 r F P 0 g s .80036 .40815 m .78223 .39265 L .82638 .37342 L p .699 .862 .96 r F P 0 g s .43975 .54204 m .46371 .56388 L .42265 .57289 L p .607 .759 .952 r F P 0 g s .42265 .57289 m .39829 .55137 L .43975 .54204 L p .607 .759 .952 r F P 0 g s .2654 .52174 m .29257 .53515 L .2523 .55312 L p .699 .862 .96 r F P 0 g s .2523 .55312 m .23949 .5471 L p .2654 .52174 L .699 .862 .96 r F P 0 g s .25197 .5572 m .23949 .5471 L p .26507 .52589 L .607 .759 .952 r F P 0 g s .23949 .5471 m .22501 .53539 L .24629 .53034 L p .607 .759 .952 r F P 0 g s .24629 .53034 m .2654 .52174 L p .23949 .5471 L .699 .862 .96 r F P 0 g s .24629 .53034 m .26507 .52589 L p .23949 .5471 L .607 .759 .952 r F P 0 g s .23949 .5471 m .22459 .54011 L .24629 .53034 L p .699 .862 .96 r F P 0 g s .83068 .56489 m .84898 .58645 L .80451 .59528 L p .607 .759 .952 r F P 0 g s .80451 .59528 m .78571 .57404 L .83068 .56489 L p .607 .759 .952 r F P 0 g s .54801 .5454 m .57046 .56725 L .52836 .57625 L p .607 .759 .952 r F P 0 g s .52836 .57625 m .50549 .55472 L .54801 .5454 L p .607 .759 .952 r F P 0 g s .41636 .47992 m .44096 .49406 L .39976 .5123 L p .699 .862 .96 r F P 0 g s .39976 .5123 m .37459 .49856 L .41636 .47992 L p .699 .862 .96 r F P 0 g s .26507 .52589 m .29168 .54804 L .25197 .5572 L p .607 .759 .952 r F P 0 g s .56763 .43802 m .58964 .45289 L .5475 .47139 L p .699 .862 .96 r F P 0 g s .5475 .47139 m .52489 .45693 L .56763 .43802 L p .699 .862 .96 r F P 0 g s .7192 .39603 m .73862 .41164 L .69554 .43041 L p .699 .862 .96 r F P 0 g s .69554 .43041 m .67548 .41522 L .7192 .39603 L p .699 .862 .96 r F P 0 g s .94029 .56832 m .95703 .58988 L .9115 .59871 L p .607 .759 .952 r F P 0 g s .9115 .59871 m .89424 .57746 L .94029 .56832 L p .607 .759 .952 r F P 0 g s .65688 .54877 m .67779 .57064 L .63465 .57963 L p .607 .759 .952 r F P 0 g s .63465 .57963 m .61329 .55809 L .65688 .54877 L p .607 .759 .952 r F P 0 g s .87107 .35395 m .88789 .37031 L .84386 .38935 L p .699 .862 .96 r F P 0 g s .84386 .38935 m .82638 .37342 L .87107 .35395 L p .699 .862 .96 r F P 0 g s .3732 .52921 m .39829 .55137 L .35755 .56053 L p .607 .759 .952 r F P 0 g s .35755 .56053 m .33208 .5387 L .3732 .52921 L p .607 .759 .952 r F P 0 g s .30671 .50316 m .33333 .51697 L .29257 .53515 L p .699 .862 .96 r F P 0 g s .29257 .53515 m .2654 .52174 L .30671 .50316 L p .699 .862 .96 r F P 0 g s .76636 .55217 m .78571 .57404 L .74152 .58303 L p .607 .759 .952 r F P 0 g s .74152 .58303 m .72168 .56148 L .76636 .55217 L p .607 .759 .952 r F P 0 g s .48194 .53255 m .50549 .55472 L .46371 .56388 L p .607 .759 .952 r F P 0 g s .46371 .56388 m .43975 .54204 L .48194 .53255 L p .607 .759 .952 r F P 0 g s .45865 .46105 m .48267 .47561 L .44096 .49406 L p .699 .862 .96 r F P 0 g s .44096 .49406 m .41636 .47992 L .45865 .46105 L p .699 .862 .96 r F P 0 g s .19725 .51291 m .22501 .53539 L .18565 .54472 L p .607 .759 .952 r F P 0 g s .18565 .54472 m .15755 .52258 L .19725 .51291 L p .607 .759 .952 r F P 0 g s .6109 .41887 m .6323 .43417 L .58964 .45289 L p .699 .862 .96 r F P 0 g s .58964 .45289 m .56763 .43802 L .6109 .41887 L p .699 .862 .96 r F P 0 g s .87645 .55558 m .89424 .57746 L .84898 .58645 L p .607 .759 .952 r F P 0 g s .84898 .58645 m .83068 .56489 L .87645 .55558 L p .607 .759 .952 r F P 0 g s .76346 .3766 m .78223 .39265 L .73862 .41164 L p .699 .862 .96 r F P 0 g s .73862 .41164 m .7192 .39603 L .76346 .3766 L p .699 .862 .96 r F P 0 g s .59129 .53591 m .61329 .55809 L .57046 .56725 L p .607 .759 .952 r F P 0 g s .57046 .56725 m .54801 .5454 L .59129 .53591 L p .607 .759 .952 r F P 0 g s .30585 .51622 m .33208 .5387 L .29168 .54804 L p .607 .759 .952 r F P 0 g s .29168 .54804 m .26507 .52589 L .30585 .51622 L p .607 .759 .952 r F P 0 g s .1959 .52663 m .22459 .54011 L .18428 .55824 L p .699 .862 .96 r F P 0 g s .18428 .55824 m .15507 .54517 L .1959 .52663 L p .699 .862 .96 r F P 0 g s .34853 .48433 m .37459 .49856 L .33333 .51697 L p .699 .862 .96 r F P 0 g s .33333 .51697 m .30671 .50316 L .34853 .48433 L p .699 .862 .96 r F P 0 g s .70125 .53929 m .72168 .56148 L .67779 .57064 L p .607 .759 .952 r F P 0 g s .67779 .57064 m .65688 .54877 L .70125 .53929 L p .607 .759 .952 r F P 0 g s .41506 .51954 m .43975 .54204 L .39829 .55137 L p .607 .759 .952 r F P 0 g s .39829 .55137 m .3732 .52921 L .41506 .51954 L p .607 .759 .952 r F P 0 g s .50147 .44195 m .52489 .45693 L .48267 .47561 L p .699 .862 .96 r F P 0 g s .48267 .47561 m .45865 .46105 L .50147 .44195 L p .699 .862 .96 r F P 0 g s .65471 .39948 m .67548 .41522 L .6323 .43417 L p .699 .862 .96 r F P 0 g s .6323 .43417 m .6109 .41887 L .65471 .39948 L p .699 .862 .96 r F P 0 g s .81183 .54268 m .83068 .56489 L .78571 .57404 L p .607 .759 .952 r F P 0 g s .78571 .57404 m .76636 .55217 L .81183 .54268 L p .607 .759 .952 r F P 0 g s .80827 .35693 m .82638 .37342 L .78223 .39265 L p .699 .862 .96 r F P 0 g s .78223 .39265 m .76346 .3766 L .80827 .35693 L p .699 .862 .96 r F P 0 g s .52489 .52289 m .54801 .5454 L .50549 .55472 L p .607 .759 .952 r F P 0 g s .50549 .55472 m .48194 .53255 L .52489 .52289 L p .607 .759 .952 r F P 0 g s .23767 .50307 m .25239 .51533 L p .22501 .53539 L .607 .759 .952 r F P 0 g s .24629 .53034 m .22501 .53539 L p .25239 .51533 L .607 .759 .952 r F P 0 g s .23726 .50786 m .25239 .51533 L p .22459 .54011 L .699 .862 .96 r F P 0 g s .25239 .51533 m .2654 .52174 L .24629 .53034 L p .699 .862 .96 r F P 0 g s .24629 .53034 m .22459 .54011 L p .25239 .51533 L .699 .862 .96 r F P 0 g s .25239 .51533 m .26507 .52589 L .24629 .53034 L p .607 .759 .952 r F P 0 g s .22501 .53539 m .19725 .51291 L .23767 .50307 L p .607 .759 .952 r F P 0 g s .22459 .54011 m .1959 .52663 L .23726 .50786 L p .699 .862 .96 r F P 0 g s .92305 .5461 m .94029 .56832 L .89424 .57746 L p .607 .759 .952 r F P 0 g s .89424 .57746 m .87645 .55558 L .92305 .5461 L p .607 .759 .952 r F P 0 g s .63534 .52625 m .65688 .54877 L .61329 .55809 L p .607 .759 .952 r F P 0 g s .61329 .55809 m .59129 .53591 L .63534 .52625 L p .607 .759 .952 r F P 0 g s .39089 .46528 m .41636 .47992 L .37459 .49856 L p .699 .862 .96 r F P 0 g s .37459 .49856 m .34853 .48433 L .39089 .46528 L p .699 .862 .96 r F P 0 g s .34736 .50638 m .3732 .52921 L .33208 .5387 L p .607 .759 .952 r F P 0 g s .33208 .5387 m .30585 .51622 L .34736 .50638 L p .607 .759 .952 r F P 0 g s .54483 .42261 m .56763 .43802 L .52489 .45693 L p .699 .862 .96 r F P 0 g s .52489 .45693 m .50147 .44195 L .54483 .42261 L p .699 .862 .96 r F P 0 g s .69908 .37985 m .7192 .39603 L .67548 .41522 L p .699 .862 .96 r F P 0 g s .67548 .41522 m .65471 .39948 L .69908 .37985 L p .699 .862 .96 r F P 0 g s .74642 .52963 m .76636 .55217 L .72168 .56148 L p .607 .759 .952 r F P 0 g s .72168 .56148 m .70125 .53929 L .74642 .52963 L p .607 .759 .952 r F P 0 g s .85365 .33701 m .87107 .35395 L .82638 .37342 L p .699 .862 .96 r F P 0 g s .82638 .37342 m .80827 .35693 L .85365 .33701 L p .699 .862 .96 r F P 0 g s .45767 .50971 m .48194 .53255 L .43975 .54204 L p .607 .759 .952 r F P 0 g s .43975 .54204 m .41506 .51954 L .45767 .50971 L p .607 .759 .952 r F P 0 g s .16865 .48976 m .19725 .51291 L .15755 .52258 L p .607 .759 .952 r F P 0 g s .15755 .52258 m .1286 .49978 L .16865 .48976 L p .607 .759 .952 r F P 0 g s .27913 .48885 m .30671 .50316 L .2654 .52174 L p .699 .862 .96 r F P 0 g s .2654 .52174 m .25239 .51533 L p .27913 .48885 L .699 .862 .96 r F P 0 g s .26507 .52589 m .25239 .51533 L p .27882 .49305 L .607 .759 .952 r F P 0 g s .25239 .51533 m .23767 .50307 L .25952 .49775 L p .607 .759 .952 r F P 0 g s .25952 .49775 m .27913 .48885 L p .25239 .51533 L .699 .862 .96 r F P 0 g s .25952 .49775 m .27882 .49305 L p .25239 .51533 L .607 .759 .952 r F P 0 g s .25239 .51533 m .23726 .50786 L .25952 .49775 L p .699 .862 .96 r F P 0 g s .85813 .53303 m .87645 .55558 L .83068 .56489 L p .607 .759 .952 r F P 0 g s .83068 .56489 m .81183 .54268 L .85813 .53303 L p .607 .759 .952 r F P 0 g s .56861 .51305 m .59129 .53591 L .54801 .5454 L p .607 .759 .952 r F P 0 g s .54801 .5454 m .52489 .52289 L .56861 .51305 L p .607 .759 .952 r F P 0 g s .43377 .44598 m .45865 .46105 L .41636 .47992 L p .699 .862 .96 r F P 0 g s .41636 .47992 m .39089 .46528 L .43377 .44598 L p .699 .862 .96 r F P 0 g s .27882 .49305 m .30585 .51622 L .26507 .52589 L p .607 .759 .952 r F P 0 g s .58873 .40302 m .6109 .41887 L .56763 .43802 L p .699 .862 .96 r F P 0 g s .56763 .43802 m .54483 .42261 L .58873 .40302 L p .699 .862 .96 r F P 0 g s .74401 .35997 m .76346 .3766 L .7192 .39603 L p .699 .862 .96 r F P 0 g s .7192 .39603 m .69908 .37985 L .74401 .35997 L p .699 .862 .96 r F P 0 g s .68019 .51641 m .70125 .53929 L .65688 .54877 L p .607 .759 .952 r F P 0 g s .65688 .54877 m .63534 .52625 L .68019 .51641 L p .607 .759 .952 r F P 0 g s .38962 .49636 m .41506 .51954 L .3732 .52921 L p .607 .759 .952 r F P 0 g s .3732 .52921 m .34736 .50638 L .38962 .49636 L p .607 .759 .952 r F P 0 g s .16618 .51267 m .1959 .52663 L .15507 .54517 L p .699 .862 .96 r F P 0 g s .15507 .54517 m .1248 .53163 L .16618 .51267 L p .699 .862 .96 r F P 0 g s .32154 .4696 m .34853 .48433 L .30671 .50316 L p .699 .862 .96 r F P 0 g s .30671 .50316 m .27913 .48885 L .32154 .4696 L p .699 .862 .96 r F P 0 g s .79241 .5198 m .81183 .54268 L .76636 .55217 L p .607 .759 .952 r F P 0 g s .76636 .55217 m .74642 .52963 L .79241 .5198 L p .607 .759 .952 r F P 0 g s .50106 .49969 m .52489 .52289 L .48194 .53255 L p .607 .759 .952 r F P 0 g s .48194 .53255 m .45767 .50971 L .50106 .49969 L p .607 .759 .952 r F P 0 g s .47721 .42643 m .50147 .44195 L .45865 .46105 L p .699 .862 .96 r F P 0 g s .45865 .46105 m .43377 .44598 L .47721 .42643 L p .699 .862 .96 r F P 0 g s .20943 .47956 m .23767 .50307 L .19725 .51291 L p .607 .759 .952 r F P 0 g s .19725 .51291 m .16865 .48976 L .20943 .47956 L p .607 .759 .952 r F P 0 g s .6332 .38318 m .65471 .39948 L .6109 .41887 L p .699 .862 .96 r F P 0 g s .6109 .41887 m .58873 .40302 L .6332 .38318 L p .699 .862 .96 r F P 0 g s .90527 .5232 m .92305 .5461 L .87645 .55558 L p .607 .759 .952 r F P 0 g s .87645 .55558 m .85813 .53303 L .90527 .5232 L p .607 .759 .952 r F P 0 g s .78951 .33984 m .80827 .35693 L .76346 .3766 L p .699 .862 .96 r F P 0 g s .76346 .3766 m .74401 .35997 L .78951 .33984 L p .699 .862 .96 r F P 0 g s .61313 .50303 m .63534 .52625 L .59129 .53591 L p .607 .759 .952 r F P 0 g s .59129 .53591 m .56861 .51305 L .61313 .50303 L p .607 .759 .952 r F P 0 g s .32072 .48285 m .34736 .50638 L .30585 .51622 L p .607 .759 .952 r F P 0 g s .30585 .51622 m .27882 .49305 L .32072 .48285 L p .607 .759 .952 r F P 0 g s .2081 .49347 m .23726 .50786 L .1959 .52663 L p .699 .862 .96 r F P 0 g s .1959 .52663 m .16618 .51267 L .2081 .49347 L p .699 .862 .96 r F P 0 g s .36448 .4501 m .39089 .46528 L .34853 .48433 L p .699 .862 .96 r F P 0 g s .34853 .48433 m .32154 .4696 L .36448 .4501 L p .699 .862 .96 r F P 0 g s .72586 .5064 m .74642 .52963 L .70125 .53929 L p .607 .759 .952 r F P 0 g s .70125 .53929 m .68019 .51641 L .72586 .5064 L p .607 .759 .952 r F P 0 g s .43265 .48616 m .45767 .50971 L .41506 .51954 L p .607 .759 .952 r F P 0 g s .41506 .51954 m .38962 .49636 L .43265 .48616 L p .607 .759 .952 r F P 0 g s .13916 .46589 m .16865 .48976 L .1286 .49978 L p .607 .759 .952 r F P 0 g s .1286 .49978 m .09877 .47628 L .13916 .46589 L p .607 .759 .952 r F P 0 g s .5212 .40664 m .54483 .42261 L .50147 .44195 L p .699 .862 .96 r F P 0 g s .50147 .44195 m .47721 .42643 L .5212 .40664 L p .699 .862 .96 r F P 0 g s .67823 .36309 m .69908 .37985 L .65471 .39948 L p .699 .862 .96 r F P 0 g s .65471 .39948 m .6332 .38318 L .67823 .36309 L p .699 .862 .96 r F P 0 g s .83924 .50979 m .85813 .53303 L .81183 .54268 L p .607 .759 .952 r F P 0 g s .81183 .54268 m .79241 .5198 L .83924 .50979 L p .607 .759 .952 r F P 0 g s .83559 .31945 m .85365 .33701 L .80827 .35693 L p .699 .862 .96 r F P 0 g s .80827 .35693 m .78951 .33984 L .83559 .31945 L p .699 .862 .96 r F P 0 g s .54524 .48948 m .56861 .51305 L .52489 .52289 L p .607 .759 .952 r F P 0 g s .52489 .52289 m .50106 .49969 L .54524 .48948 L p .607 .759 .952 r F P 0 g s .25095 .46916 m .26592 .482 L p .23767 .50307 L .607 .759 .952 r F P 0 g s .25952 .49775 m .23767 .50307 L p .26592 .482 L .607 .759 .952 r F P 0 g s .25055 .47402 m .26592 .482 L p .23726 .50786 L .699 .862 .96 r F P 0 g s .26592 .482 m .27913 .48885 L .25952 .49775 L p .699 .862 .96 r F P 0 g s .25952 .49775 m .23726 .50786 L p .26592 .482 L .699 .862 .96 r F P 0 g s .26592 .482 m .27882 .49305 L .25952 .49775 L p .607 .759 .952 r F P 0 g s .23767 .50307 m .20943 .47956 L .25095 .46916 L p .607 .759 .952 r F P 0 g s .23726 .50786 m .2081 .49347 L .25055 .47402 L p .699 .862 .96 r F P 0 g s .65848 .49283 m .68019 .51641 L .63534 .52625 L p .607 .759 .952 r F P 0 g s .63534 .52625 m .61313 .50303 L .65848 .49283 L p .607 .759 .952 r F P 0 g s .40799 .43035 m .43377 .44598 L .39089 .46528 L p .699 .862 .96 r F P 0 g s .39089 .46528 m .36448 .4501 L .40799 .43035 L p .699 .862 .96 r F P 0 g s .36339 .47246 m .38962 .49636 L .34736 .50638 L p .607 .759 .952 r F P 0 g s .34736 .50638 m .32072 .48285 L .36339 .47246 L p .607 .759 .952 r F P 0 g s .56575 .38659 m .58873 .40302 L .54483 .42261 L p .699 .862 .96 r F P 0 g s .54483 .42261 m .5212 .40664 L .56575 .38659 L p .699 .862 .96 r F P 0 g s .72385 .34274 m .74401 .35997 L .69908 .37985 L p .699 .862 .96 r F P 0 g s .69908 .37985 m .67823 .36309 L .72385 .34274 L p .699 .862 .96 r F P 0 g s .77237 .4962 m .79241 .5198 L .74642 .52963 L p .607 .759 .952 r F P 0 g s .74642 .52963 m .72586 .5064 L .77237 .4962 L p .607 .759 .952 r F P 0 g s .47648 .47576 m .50106 .49969 L .45767 .50971 L p .607 .759 .952 r F P 0 g s .45767 .50971 m .43265 .48616 L .47648 .47576 L p .607 .759 .952 r F P 0 g s .1803 .45531 m .20943 .47956 L .16865 .48976 L p .607 .759 .952 r F P 0 g s .16865 .48976 m .13916 .46589 L .1803 .45531 L p .607 .759 .952 r F P 0 g s .13537 .4982 m .16618 .51267 L .1248 .53163 L p .699 .862 .96 r F P 0 g s .1248 .53163 m .09343 .5176 L .13537 .4982 L p .699 .862 .96 r F P 0 g s .29355 .45432 m .32154 .4696 L .27913 .48885 L p .699 .862 .96 r F P 0 g s .27913 .48885 m .26592 .482 L p .29355 .45432 L .699 .862 .96 r F P 0 g s .27882 .49305 m .26592 .482 L p .29325 .45858 L .607 .759 .952 r F P 0 g s .26592 .482 m .25095 .46916 L .27341 .46354 L p .607 .759 .952 r F P 0 g s .27341 .46354 m .29355 .45432 L p .26592 .482 L .699 .862 .96 r F P 0 g s .27341 .46354 m .29325 .45858 L p .26592 .482 L .607 .759 .952 r F P 0 g s .26592 .482 m .25055 .47402 L .27341 .46354 L p .699 .862 .96 r F P 0 g s .88694 .49959 m .90527 .5232 L .85813 .53303 L p .607 .759 .952 r F P 0 g s .85813 .53303 m .83924 .50979 L .88694 .49959 L p .607 .759 .952 r F P 0 g s .59024 .47909 m .61313 .50303 L .56861 .51305 L p .607 .759 .952 r F P 0 g s .56861 .51305 m .54524 .48948 L .59024 .47909 L p .607 .759 .952 r F P 0 g s .45205 .41035 m .47721 .42643 L .43377 .44598 L p .699 .862 .96 r F P 0 g s .43377 .44598 m .40799 .43035 L .45205 .41035 L p .699 .862 .96 r F P 0 g s .29325 .45858 m .32072 .48285 L .27882 .49305 L p .607 .759 .952 r F P 0 g s .61089 .36628 m .6332 .38318 L .58873 .40302 L p .699 .862 .96 r F P 0 g s .58873 .40302 m .56575 .38659 L .61089 .36628 L p .699 .862 .96 r F P 0 g s .77005 .32212 m .78951 .33984 L .74401 .35997 L p .699 .862 .96 r F P 0 g s .74401 .35997 m .72385 .34274 L .77005 .32212 L p .699 .862 .96 r F P 0 g s .70466 .48244 m .72586 .5064 L .68019 .51641 L p .607 .759 .952 r F P 0 g s .68019 .51641 m .65848 .49283 L .70466 .48244 L p .607 .759 .952 r F P 0 g s .40685 .46187 m .43265 .48616 L .38962 .49636 L p .607 .759 .952 r F P 0 g s .38962 .49636 m .36339 .47246 L .40685 .46187 L p .607 .759 .952 r F P 0 g s .10876 .44128 m .13916 .46589 L .09877 .47628 L p .607 .759 .952 r F P 0 g s .09877 .47628 m .06802 .45206 L .10876 .44128 L p .607 .759 .952 r F P 0 g s .17786 .47855 m .2081 .49347 L .16618 .51267 L p .699 .862 .96 r F P 0 g s .16618 .51267 m .13537 .4982 L .17786 .47855 L p .699 .862 .96 r F P 0 g s .33711 .43436 m .36448 .4501 L .32154 .4696 L p .699 .862 .96 r F P 0 g s .32154 .4696 m .29355 .45432 L .33711 .43436 L p .699 .862 .96 r F P 0 g s .81976 .48581 m .83924 .50979 L .79241 .5198 L p .607 .759 .952 r F P 0 g s .79241 .5198 m .77237 .4962 L .81976 .48581 L p .607 .759 .952 r F P 0 g s .52113 .46518 m .54524 .48948 L .50106 .49969 L p .607 .759 .952 r F P 0 g s .50106 .49969 m .47648 .47576 L .52113 .46518 L p .607 .759 .952 r F P 0 g s .49669 .39008 m .5212 .40664 L .47721 .42643 L p .699 .862 .96 r F P 0 g s .47721 .42643 m .45205 .41035 L .49669 .39008 L p .699 .862 .96 r F P 0 g s .22221 .44453 m .25095 .46916 L .20943 .47956 L p .607 .759 .952 r F P 0 g s .20943 .47956 m .1803 .45531 L .22221 .44453 L p .607 .759 .952 r F P 0 g s .65661 .34571 m .67823 .36309 L .6332 .38318 L p .699 .862 .96 r F P 0 g s .6332 .38318 m .61089 .36628 L .65661 .34571 L p .699 .862 .96 r F P 0 g s .81687 .30124 m .83559 .31945 L .78951 .33984 L p .699 .862 .96 r F P 0 g s .78951 .33984 m .77005 .32212 L .81687 .30124 L p .699 .862 .96 r F P 0 g s .63608 .46851 m .65848 .49283 L .61313 .50303 L p .607 .759 .952 r F P 0 g s .61313 .50303 m .59024 .47909 L .63608 .46851 L p .607 .759 .952 r F P 0 g s .33633 .4478 m .36339 .47246 L .32072 .48285 L p .607 .759 .952 r F P 0 g s .32072 .48285 m .29325 .45858 L .33633 .4478 L p .607 .759 .952 r F P 0 g s .2209 .45864 m .25055 .47402 L .2081 .49347 L p .699 .862 .96 r F P 0 g s .2081 .49347 m .17786 .47855 L .2209 .45864 L p .699 .862 .96 r F P 0 g s .38124 .41414 m .40799 .43035 L .36448 .4501 L p .699 .862 .96 r F P 0 g s .36448 .4501 m .33711 .43436 L .38124 .41414 L p .699 .862 .96 r F P 0 g s .75171 .47186 m .77237 .4962 L .72586 .5064 L p .607 .759 .952 r F P 0 g s .72586 .5064 m .70466 .48244 L .75171 .47186 L p .607 .759 .952 r F P 0 g s .45113 .45109 m .47648 .47576 L .43265 .48616 L p .607 .759 .952 r F P 0 g s .43265 .48616 m .40685 .46187 L .45113 .45109 L p .607 .759 .952 r F P 0 g s .15026 .4303 m .1803 .45531 L .13916 .46589 L p .607 .759 .952 r F P 0 g s .13916 .46589 m .10876 .44128 L .15026 .4303 L p .607 .759 .952 r F P 0 g s .54192 .36955 m .56575 .38659 L .5212 .40664 L p .699 .862 .96 r F P 0 g s .5212 .40664 m .49669 .39008 L .54192 .36955 L p .699 .862 .96 r F P 0 g s .70293 .32486 m .72385 .34274 L .67823 .36309 L p .699 .862 .96 r F P 0 g s .67823 .36309 m .65661 .34571 L .70293 .32486 L p .699 .862 .96 r F P 0 g s .86803 .47523 m .88694 .49959 L .83924 .50979 L p .607 .759 .952 r F P 0 g s .83924 .50979 m .81976 .48581 L .86803 .47523 L p .607 .759 .952 r F P 0 g s .56662 .4544 m .59024 .47909 L .54524 .48948 L p .607 .759 .952 r F P 0 g s .54524 .48948 m .52113 .46518 L .56662 .4544 L p .607 .759 .952 r F P 0 g s .2649 .43354 m .28013 .44699 L p .25095 .46916 L .607 .759 .952 r F P 0 g s .27341 .46354 m .25095 .46916 L p .28013 .44699 L .607 .759 .952 r F P 0 g s .26451 .43847 m .28013 .44699 L p .25055 .47402 L .699 .862 .96 r F P 0 g s .28013 .44699 m .29355 .45432 L .27341 .46354 L p .699 .862 .96 r F P 0 g s .27341 .46354 m .25055 .47402 L p .28013 .44699 L .699 .862 .96 r F P 0 g s .28013 .44699 m .29325 .45858 L .27341 .46354 L p .607 .759 .952 r F P 0 g s .25095 .46916 m .22221 .44453 L .2649 .43354 L p .607 .759 .952 r F P 0 g s .10341 .48319 m .13537 .4982 L .09343 .5176 L p .699 .862 .96 r F P 0 g s .09343 .5176 m .0609 .50304 L .10341 .48319 L p .699 .862 .96 r F P 0 g s .25055 .47402 m .2209 .45864 L .26451 .43847 L p .699 .862 .96 r F P 0 g s .68279 .45772 m .70466 .48244 L .65848 .49283 L p .607 .759 .952 r F P 0 g s .65848 .49283 m .63608 .46851 L .68279 .45772 L p .607 .759 .952 r F P 0 g s .42595 .39365 m .45205 .41035 L .40799 .43035 L p .699 .862 .96 r F P 0 g s .40799 .43035 m .38124 .41414 L .42595 .39365 L p .699 .862 .96 r F P 0 g s .38023 .43681 m .40685 .46187 L .36339 .47246 L p .607 .759 .952 r F P 0 g s .36339 .47246 m .33633 .4478 L .38023 .43681 L p .607 .759 .952 r F P 0 g s .07738 .41588 m .10876 .44128 L .06802 .45206 L p .607 .759 .952 r F P 0 g s .06802 .45206 m .03629 .42707 L .07738 .41588 L p .607 .759 .952 r F P 0 g s .58774 .34875 m .61089 .36628 L .56575 .38659 L p .699 .862 .96 r F P 0 g s .56575 .38659 m .54192 .36955 L .58774 .34875 L p .699 .862 .96 r F P 0 g s .74987 .30374 m .77005 .32212 L .72385 .34274 L p .699 .862 .96 r F P 0 g s .72385 .34274 m .70293 .32486 L .74987 .30374 L p .699 .862 .96 r F P 0 g s .79965 .46107 m .81976 .48581 L .77237 .4962 L p .607 .759 .952 r F P 0 g s .77237 .4962 m .75171 .47186 L .79965 .46107 L p .607 .759 .952 r F P 0 g s .49625 .4401 m .52113 .46518 L .47648 .47576 L p .607 .759 .952 r F P 0 g s .47648 .47576 m .45113 .45109 L .49625 .4401 L p .607 .759 .952 r F P 0 g s .19255 .41911 m .22221 .44453 L .1803 .45531 L p .607 .759 .952 r F P 0 g s .1803 .45531 m .15026 .4303 L .19255 .41911 L p .607 .759 .952 r F P 0 g s .14648 .46307 m .17786 .47855 L .13537 .4982 L p .699 .862 .96 r F P 0 g s .13537 .4982 m .10341 .48319 L .14648 .46307 L p .699 .862 .96 r F P 0 g s .3087 .41803 m .33711 .43436 L .29355 .45432 L p .699 .862 .96 r F P 0 g s .29355 .45432 m .28013 .44699 L p .3087 .41803 L .699 .862 .96 r F P 0 g s .29325 .45858 m .28013 .44699 L p .30841 .42235 L .607 .759 .952 r F P 0 g s .28013 .44699 m .2649 .43354 L .28801 .4276 L p .607 .759 .952 r F P 0 g s .28801 .4276 m .3087 .41803 L p .28013 .44699 L .699 .862 .96 r F P 0 g s .28801 .4276 m .30841 .42235 L p .28013 .44699 L .607 .759 .952 r F P 0 g s .28013 .44699 m .26451 .43847 L .28801 .4276 L p .699 .862 .96 r F P 0 g s .61297 .44341 m .63608 .46851 L .59024 .47909 L p .607 .759 .952 r F P 0 g s .59024 .47909 m .56662 .4544 L .61297 .44341 L p .607 .759 .952 r F P 0 g s .47126 .3729 m .49669 .39008 L .45205 .41035 L p .699 .862 .96 r F P 0 g s .45205 .41035 m .42595 .39365 L .47126 .3729 L p .699 .862 .96 r F P 0 g s .30841 .42235 m .33633 .4478 L .29325 .45858 L p .607 .759 .952 r F P 0 g s .63417 .32767 m .65661 .34571 L .61089 .36628 L p .699 .862 .96 r F P 0 g s .61089 .36628 m .58774 .34875 L .63417 .32767 L p .699 .862 .96 r F P 0 g s .79743 .28234 m .81687 .30124 L .77005 .32212 L p .699 .862 .96 r F P 0 g s .77005 .32212 m .74987 .30374 L .79743 .28234 L p .699 .862 .96 r F P 0 g s .73038 .44673 m .75171 .47186 L .70466 .48244 L p .607 .759 .952 r F P 0 g s .70466 .48244 m .68279 .45772 L .73038 .44673 L p .607 .759 .952 r F P 0 g s .42497 .42562 m .45113 .45109 L .40685 .46187 L p .607 .759 .952 r F P 0 g s .40685 .46187 m .38023 .43681 L .42497 .42562 L p .607 .759 .952 r F P 0 g s .11925 .40448 m .15026 .4303 L .10876 .44128 L p .607 .759 .952 r F P 0 g s .10876 .44128 m .07738 .41588 L .11925 .40448 L p .607 .759 .952 r F P 0 g s .19013 .44268 m .2209 .45864 L .17786 .47855 L p .699 .862 .96 r F P 0 g s .17786 .47855 m .14648 .46307 L .19013 .44268 L p .699 .862 .96 r F P 0 g s .35348 .39732 m .38124 .41414 L .33711 .43436 L p .699 .862 .96 r F P 0 g s .33711 .43436 m .3087 .41803 L .35348 .39732 L p .699 .862 .96 r F P 0 g s .84851 .45008 m .86803 .47523 L .81976 .48581 L p .607 .759 .952 r F P 0 g s .81976 .48581 m .79965 .46107 L .84851 .45008 L p .607 .759 .952 r F P 0 g s .54223 .4289 m .56662 .4544 L .52113 .46518 L p .607 .759 .952 r F P 0 g s .52113 .46518 m .49625 .4401 L .54223 .4289 L p .607 .759 .952 r F P 0 g s .51717 .35186 m .54192 .36955 L .49669 .39008 L p .699 .862 .96 r F P 0 g s .49669 .39008 m .47126 .3729 L .51717 .35186 L p .699 .862 .96 r F P 0 g s .23565 .4077 m .2649 .43354 L .22221 .44453 L p .607 .759 .952 r F P 0 g s .22221 .44453 m .19255 .41911 L .23565 .4077 L p .607 .759 .952 r F P 0 g s .68123 .3063 m .70293 .32486 L .65661 .34571 L p .699 .862 .96 r F P 0 g s .65661 .34571 m .63417 .32767 L .68123 .3063 L p .699 .862 .96 r F P 0 g s .66021 .43221 m .68279 .45772 L .63608 .46851 L p .607 .759 .952 r F P 0 g s .63608 .46851 m .61297 .44341 L .66021 .43221 L p .607 .759 .952 r F P 0 g s .35275 .41094 m .38023 .43681 L .33633 .4478 L p .607 .759 .952 r F P 0 g s .33633 .4478 m .30841 .42235 L .35275 .41094 L p .607 .759 .952 r F P 0 g s .07023 .4676 m .10341 .48319 L .0609 .50304 L p .699 .862 .96 r F P 0 g s .0609 .50304 m .02714 .48794 L .07023 .4676 L p .699 .862 .96 r F P 0 g s .23437 .42201 m .26451 .43847 L .2209 .45864 L p .699 .862 .96 r F P 0 g s .2209 .45864 m .19013 .44268 L .23437 .42201 L p .699 .862 .96 r F P 0 g s .39886 .37633 m .42595 .39365 L .38124 .41414 L p .699 .862 .96 r F P 0 g s .38124 .41414 m .35348 .39732 L .39886 .37633 L p .699 .862 .96 r F P 0 g s .7789 .43553 m .79965 .46107 L .75171 .47186 L p .607 .759 .952 r F P 0 g s .75171 .47186 m .73038 .44673 L .7789 .43553 L p .607 .759 .952 r F P 0 g s .47057 .41421 m .49625 .4401 L .45113 .45109 L p .607 .759 .952 r F P 0 g s .45113 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De la \ longitud total de la pieza, ", Cell[BoxData[ FormBox["x", TraditionalForm]]], " m los colorea verde, ", Cell[BoxData[ FormBox["y", TraditionalForm]]], " m amarillo y ", Cell[BoxData[ FormBox["z", TraditionalForm]]], " m de rojo. El coste esta dado por " }], "Text", FontSize->16], Cell[BoxData[ RowBox[{ RowBox[{"c", RowBox[{"(", RowBox[{"x", ",", "y", ",", "z"}], ")"}]}], "=", RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"x", "+", RowBox[{"2", "z"}]}], ")"}], "2"], "+", RowBox[{"200", "y"}]}]}]], "Text", FontSize->16], Cell["\<\ La demanda del color rojo es el doble que para el verde. \ \[DownQuestion]Cuantos metros hay que colorear de cada color para minimizar \ el coste?. \ \>", "Text", FontSize->16], Cell[CellGroupData[{ Cell["Sol.:", "Subsubsection"], Cell["Del enunciado se obtiene las siguientes restricciones:", "Text", FontSize->16], Cell[TextData[{ "(a)", Cell[BoxData[ FormBox[ RowBox[{"\t", RowBox[{ RowBox[{"x", " ", "+", " ", "y", " ", "+", " ", "z"}], " ", "=", " ", RowBox[{ RowBox[{"50", " ", "\[Rule]", " ", "z"}], " ", "=", " ", RowBox[{"50", " ", "-", " ", "x", "-", " ", "y"}]}]}]}], TraditionalForm]]], "\n(b)", Cell[BoxData[ FormBox[ RowBox[{"\t", RowBox[{"z", " ", "=", " ", RowBox[{ RowBox[{ RowBox[{"2", " ", "x"}], " ", "\[Rule]", " ", RowBox[{"z", "-", RowBox[{"2", " ", "x"}]}]}], " ", "=", " ", "0"}]}]}], TraditionalForm]]] }], "Text", FontSize->16], Cell["\<\ El problema es inicialmente de tres variables, sin embargo una de las \ variables puede expresarse en funci\[OAcute]n de las otras lo que simplifica \ el problema. En efecto. La condicion (a) podemos reescribirla como:\ \>", "Text"], Cell[TextData[{ Cell[BoxData[ FormBox[ RowBox[{"\t", RowBox[{ RowBox[{"x", " ", "+", " ", "y", " ", "+", " ", "z"}], " ", "=", " ", RowBox[{ RowBox[{"50", " ", "\[Rule]", " ", "z"}], " ", "=", " ", RowBox[{"50", " ", "-", " ", "x", "-", " ", "y"}]}]}]}], TraditionalForm]]], "\nEntonces reemplazamos z en (b) y y en ", Cell[BoxData[ FormBox[ RowBox[{"c", "(", RowBox[{"x", ",", "y", ",", "z"}], ")"}], TraditionalForm]]], " y nos quedan\n", Cell[BoxData[ FormBox[ RowBox[{"\t", RowBox[{"z", " ", "=", " ", RowBox[{ RowBox[{ RowBox[{"2", " ", "x"}], " ", "\[Rule]", " ", RowBox[{"z", "-", RowBox[{"2", " ", "x"}]}]}], " ", "=", " ", "0"}]}]}], TraditionalForm]]], " \[Rule] ", Cell[BoxData[ FormBox[ RowBox[{" ", RowBox[{ RowBox[{"\[CurlyPhi]", "(", RowBox[{"x", ",", "y"}], ")"}], "=", RowBox[{ RowBox[{"50", " ", "-", " ", RowBox[{"3", " ", "x"}], "-", " ", "y"}], " ", "=", " ", "0"}]}]}], TraditionalForm]]], " " }], "Text", FontSize->16], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"c1", "[", RowBox[{"x_", ",", "y_"}], "]"}], "=", RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"x", "+", RowBox[{"2", RowBox[{"(", " ", RowBox[{"50", " ", "-", " ", "x", "-", " ", "y"}], ")"}]}]}], ")"}], "2"], "+", RowBox[{"200", "y"}]}]}], ";"}]], "Input", FontSize->16] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Sol.: M\[EAcute]todo de los multiplicadores de Lagrange\ \>", "Subsubsection"], Cell["\<\ Construimos la funci\[OAcute]n lagrangiana\ \>", "Text", FontSize->16], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"w", "[", RowBox[{"x_", ",", "y_"}], "]"}], "=", RowBox[{ RowBox[{"c1", "[", RowBox[{"x", ",", "y"}], "]"}], "-", " ", RowBox[{"\[Lambda]", " ", RowBox[{"(", RowBox[{"50", " ", "-", " ", RowBox[{"3", " ", "x"}], "-", " ", "y"}], ")"}]}]}]}]], "Input"], Cell[BoxData[ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"x", "+", RowBox[{"2", " ", RowBox[{"(", RowBox[{"50", "-", "x", "-", "y"}], ")"}]}]}], ")"}], "2"], "+", RowBox[{"200", " ", "y"}], "-", RowBox[{ RowBox[{"(", RowBox[{"50", "-", RowBox[{"3", " ", "x"}], "-", "y"}], ")"}], " ", "\[Lambda]"}]}]], "Output", FontSize->16] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ FormBox[ RowBox[{"eq1", "=", RowBox[{ FractionBox[ RowBox[{"\[PartialD]", RowBox[{"w", "(", RowBox[{"x", ",", "y"}], ")"}]}], RowBox[{"\[PartialD]", "x"}], MultilineFunction->None], "==", "0"}]}], TraditionalForm]], "Input"], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ RowBox[{"3", " ", "\[Lambda]"}], "-", RowBox[{"2", " ", RowBox[{"(", RowBox[{"x", "+", RowBox[{"2", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "x"}], "-", "y", "+", "50"}], ")"}]}]}], ")"}]}]}], "==", "0"}], TraditionalForm]], "Output", FontSize->16] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ FormBox[ RowBox[{"eq2", "=", RowBox[{ FractionBox[ RowBox[{"\[PartialD]", RowBox[{"w", "(", RowBox[{"x", ",", "y"}], ")"}]}], RowBox[{"\[PartialD]", "y"}], MultilineFunction->None], "==", "0"}]}], TraditionalForm]], "Input"], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "4"}], " ", RowBox[{"(", RowBox[{"x", "+", RowBox[{"2", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "x"}], "-", "y", "+", "50"}], ")"}]}]}], ")"}]}], "+", "\[Lambda]", "+", "200"}], "==", "0"}], TraditionalForm]], "Output", FontSize->16] }, Open ]], Cell[TextData[{ "De las eq1 y eq2 y de la condicion \[CurlyPhi](x,y)= 0 determinamos ", Cell[BoxData[ FormBox[ RowBox[{"x", ",", " ", "y", ",", " ", "\[Lambda]", " "}], TraditionalForm]]] }], "Text", FontSize->16], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"Solve", "[", RowBox[{ RowBox[{"{", RowBox[{"eq1", ",", " ", "eq2", ",", " ", RowBox[{ RowBox[{"50", " ", "-", " ", "x", "-", " ", "y", "-", RowBox[{"2", " ", "x"}]}], " ", "==", " ", "0"}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"x", ",", " ", "y", ",", " ", "\[Lambda]"}], "}"}]}], "]"}], " "}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", "12"}], ",", RowBox[{"y", "\[Rule]", "14"}], ",", RowBox[{"\[Lambda]", "\[Rule]", "40"}]}], "}"}], "}"}]], "Output"] }, Open ]], Cell["\<\ Por tanto el menos coste se obtiene coloreando 12 m de verde, 14 m amarillo y \ 24 m (recuerdese que z = 50 - 14-12) rojo\ \>", "Text"], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"A", "=", RowBox[{ FractionBox[ RowBox[{ SuperscriptBox["\[PartialD]", "2"], RowBox[{"w", "(", RowBox[{"x", ",", "y"}], ")"}]}], RowBox[{"\[PartialD]", SuperscriptBox["x", "2"]}], MultilineFunction->None], "=", "1"}]}], ";", RowBox[{"c", "=", RowBox[{ FractionBox[ RowBox[{ SuperscriptBox["\[PartialD]", "2"], RowBox[{"w", "(", RowBox[{"x", ",", "y"}], ")"}]}], RowBox[{"\[PartialD]", SuperscriptBox["y", "2"]}], MultilineFunction->None], "=", "8"}]}], ";", RowBox[{"B", "=", RowBox[{ FractionBox[ RowBox[{ SuperscriptBox["\[PartialD]", "2"], RowBox[{"w", "(", RowBox[{"x", ",", "y"}], ")"}]}], RowBox[{ RowBox[{"\[PartialD]", "x"}], "\[ThinSpace]", RowBox[{"\[PartialD]", "y"}]}], MultilineFunction->None], "=", "4"}]}]}], TraditionalForm]], "Input"], Cell[BoxData[ RowBox[{"\[CapitalDelta]", " ", "=", " ", RowBox[{ RowBox[{ RowBox[{"A", " ", "c"}], " ", "-", " ", SuperscriptBox["B", "2"]}], "=", "0"}]}]], "Input"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"w", "[", RowBox[{"20", ",", "10"}], "]"}], "/.", RowBox[{"\[Lambda]", "\[Rule]", "40"}]}]], "Input"], Cell[BoxData["6400"], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"w", "[", RowBox[{"10", ",", "20"}], "]"}], "/.", RowBox[{"\[Lambda]", "\[Rule]", "40"}]}]], "Input"], Cell[BoxData["6500"], "Output"] }, Open ]], Cell["\<\ Para \[CapitalDelta] =0 , por tanto no podemos asegurar nada. Aunque no es \ una demostraci\[OAcute]n rigurosa podemos hacer una prueba.\ \>", "Text", FontSize->16] }, Open ]], Cell[CellGroupData[{ Cell["Sol.: M\[EAcute]todo de sustitucion", "Subsubsection"], Cell["La funcion a optimizar es", "Text", FontSize->16], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"c", "[", RowBox[{"x_", ",", "y_", ",", "z_"}], "]"}], "=", RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"x", "+", RowBox[{"2", "z"}]}], ")"}], "2"], "+", RowBox[{"200", "y"}]}]}], ";"}]], "Input"], Cell[TextData[{ "En la condicion despejamos ", Cell[BoxData[ FormBox["y", TraditionalForm]]], " " }], "Text", FontSize->16], Cell[TextData[{ "De la primera condicion ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"x", "+", "y", "+", "z"}], "=", RowBox[{ RowBox[{"50", "\[Rule]", "y"}], "=", RowBox[{"50", "-", "x", "-", "z"}]}]}], TraditionalForm]]] }], "Text", FontSize->16], Cell[BoxData[{ FormBox[ RowBox[{ RowBox[{ RowBox[{ "De", " ", "la", " ", "segunda", " ", "condici\[OAcute]n", " ", "z"}], " ", "=", 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Estudiemos las condiones proximas a (0,0). \nf(x, 0) = ", Cell[BoxData[ FormBox[ SuperscriptBox["x", "2"], TraditionalForm]]], " que toma siempre valores positivos \nf(0, y) = -", Cell[BoxData[ FormBox[ SuperscriptBox["y", "2"], TraditionalForm]]], " que toma siempre valores negativos\nEs decir: \nla funcion toma valores \ positivos en ambas direcciones del eje OX que van aumentando a medida que nos \ alejamos del origen.\nla funcion toma valores negativos en ambas direcciones \ del eje OY que van aumentando (cada vez mas negativos) a medida que nos \ alejamos del origen.\nEn conclusi\[OAcute]n; (0,0) es un punto de silla" }], "Text", FontSize->16], Cell["\<\ La representaci\[OAcute]n gr\[AAcute]fica muestra claramente que (0,0) es un \ punto de silla\ \>", "Text", FontSize->16], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Plot3D", "[", RowBox[{ RowBox[{"f", "[", RowBox[{"x", ",", "y"}], "]"}], ",", " ", RowBox[{"{", RowBox[{"x", ",", " ", RowBox[{"-", "100"}], ",", " ", "100"}], 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