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Cell[BoxData[ FormBox[ RowBox[{"z", "\[GreaterEqual]", "0"}], TraditionalForm]], "InlineMath"], ". 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Null); Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellID->133531099] }, Open ]], Cell[CellGroupData[{ Cell["", "SnapshotsSection"], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`obj$$ = False, $CellContext`objfunvalue$$ = 200, $CellContext`planes$$ = False, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`planes$$], False, "show planes"}, {True, False}}, {{ Hold[$CellContext`obj$$], False, "hide objective function plane"}, { True, False}}, {{ Hold[$CellContext`objfunvalue$$], 200, "objective function value"}, 80, 240, 10}}, Typeset`size$$ = Automatic, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`planes$252147$$ = False, $CellContext`obj$252148$$ = False, $CellContext`objfunvalue$252149$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`obj$$ = False, $CellContext`objfunvalue$$ = 200, $CellContext`planes$$ = False}, "ControllerVariables" :> { Hold[$CellContext`planes$$, $CellContext`planes$252147$$, False], Hold[$CellContext`obj$$, $CellContext`obj$252148$$, False], Hold[$CellContext`objfunvalue$$, $CellContext`objfunvalue$252149$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> If[$CellContext`planes$$, If[$CellContext`obj$$, Show[$CellContext`region1, $CellContext`region2, \ $CellContext`region3, $CellContext`options], Show[$CellContext`region1, $CellContext`region2, \ $CellContext`region3, Plot3D[ $CellContext`z[$CellContext`objfunvalue$$], {$CellContext`x, 0, 100}, {$CellContext`y, 0, 100}, Mesh -> None, PlotStyle -> Green, ClippingStyle -> None, PerformanceGoal -> "Quality"], $CellContext`options]], If[$CellContext`obj$$, Show[$CellContext`feasibleregion, $CellContext`options], Show[$CellContext`feasibleregion, Plot3D[ $CellContext`z[$CellContext`objfunvalue$$], {$CellContext`x, 0, 100}, {$CellContext`y, 0, 100}, Mesh -> None, PlotStyle -> Green, ClippingStyle -> None], $CellContext`options]]], "Specifications" :> {{{$CellContext`planes$$, False, "show planes"}, { True, False}}, {{$CellContext`obj$$, False, "hide objective function plane"}, { True, False}}, {{$CellContext`objfunvalue$$, 200, "objective function value"}, 80, 240, 10, Appearance -> "Labeled"}}, "Options" :> {}, "DefaultOptions" :> {ControllerLinking -> True}], SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>(($CellContext`options = {AxesLabel -> { Style["x", Italic], Style["y", Italic], Style["z", Italic]}, BoxRatios -> Automatic, SphericalRegion -> True, ViewPoint -> {-0.9, -1.1, 0}, PlotRange -> {{0, 100}, {0, 100}, {0, 100}}, ImageSize -> {450, 400}, PlotRangePadding -> Scaled[0.02]}; $CellContext`region1 = Plot3D[500/9 - $CellContext`x/3 - 5 ($CellContext`y/9), {$CellContext`x, 0, 100}, {$CellContext`y, 0, 100}, PlotStyle -> LightBlue, Lighting -> "Neutral", ClippingStyle -> None, Evaluate[$CellContext`options]]; $CellContext`region2 = Plot3D[70 - 4 ($CellContext`x/5), {$CellContext`x, 0, 100}, {$CellContext`y, 0, 100}, PlotStyle -> Orange, Lighting -> "Neutral", ClippingStyle -> None, Evaluate[$CellContext`options]]; $CellContext`region3 = Plot3D[50 - 2 ($CellContext`y/3), {$CellContext`x, 0, 100}, {$CellContext`y, 0, 100}, PlotStyle -> Purple, Lighting -> "Neutral", ClippingStyle -> None, Evaluate[$CellContext`options]]; $CellContext`z[ Pattern[$CellContext`t, Blank[]]] := $CellContext`t/3 - 2 ($CellContext`x/3) - $CellContext`y/2; $CellContext`feasibleregion = RegionPlot3D[ And[ 3 $CellContext`x + 5 $CellContext`y + 9 $CellContext`z <= 500, 4 $CellContext`x + 5 $CellContext`z <= 350, 2 $CellContext`y + 3 $CellContext`z <= 150], {$CellContext`x, 0, 100}, {$CellContext`y, 0, 100}, {$CellContext`z, 0, 100}, Mesh -> None, PlotStyle -> Directive[ Opacity[0.5], Red], Evaluate[$CellContext`options]]; Null); Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellID->196470505], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`obj$$ = True, $CellContext`objfunvalue$$ = 200, $CellContext`planes$$ = True, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`planes$$], True, "show planes"}, {True, False}}, {{ Hold[$CellContext`obj$$], True, "hide objective function plane"}, { True, False}}, {{ Hold[$CellContext`objfunvalue$$], 200, "objective function value"}, 80, 240, 10}}, Typeset`size$$ = Automatic, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`planes$252209$$ = False, $CellContext`obj$252210$$ = False, $CellContext`objfunvalue$252211$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`obj$$ = True, $CellContext`objfunvalue$$ = 200, $CellContext`planes$$ = True}, "ControllerVariables" :> { Hold[$CellContext`planes$$, $CellContext`planes$252209$$, False], Hold[$CellContext`obj$$, $CellContext`obj$252210$$, False], Hold[$CellContext`objfunvalue$$, $CellContext`objfunvalue$252211$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> If[$CellContext`planes$$, If[$CellContext`obj$$, Show[$CellContext`region1, $CellContext`region2, \ $CellContext`region3, $CellContext`options], Show[$CellContext`region1, $CellContext`region2, \ $CellContext`region3, Plot3D[ $CellContext`z[$CellContext`objfunvalue$$], {$CellContext`x, 0, 100}, {$CellContext`y, 0, 100}, Mesh -> None, PlotStyle -> Green, ClippingStyle -> None, PerformanceGoal -> "Quality"], $CellContext`options]], If[$CellContext`obj$$, Show[$CellContext`feasibleregion, $CellContext`options], Show[$CellContext`feasibleregion, Plot3D[ $CellContext`z[$CellContext`objfunvalue$$], {$CellContext`x, 0, 100}, {$CellContext`y, 0, 100}, Mesh -> None, PlotStyle -> Green, ClippingStyle -> None], $CellContext`options]]], "Specifications" :> {{{$CellContext`planes$$, True, "show planes"}, { True, False}}, {{$CellContext`obj$$, True, "hide objective function plane"}, { True, False}}, {{$CellContext`objfunvalue$$, 200, "objective function value"}, 80, 240, 10, Appearance -> "Labeled"}}, "Options" :> {}, "DefaultOptions" :> {ControllerLinking -> True}], SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>(($CellContext`options = {AxesLabel -> { Style["x", Italic], Style["y", Italic], Style["z", Italic]}, BoxRatios -> Automatic, SphericalRegion -> True, ViewPoint -> {-0.9, -1.1, 0}, PlotRange -> {{0, 100}, {0, 100}, {0, 100}}, ImageSize -> {450, 400}, PlotRangePadding -> Scaled[0.02]}; $CellContext`region1 = Plot3D[500/9 - $CellContext`x/3 - 5 ($CellContext`y/9), {$CellContext`x, 0, 100}, {$CellContext`y, 0, 100}, PlotStyle -> LightBlue, Lighting -> "Neutral", ClippingStyle -> None, Evaluate[$CellContext`options]]; $CellContext`region2 = Plot3D[70 - 4 ($CellContext`x/5), {$CellContext`x, 0, 100}, {$CellContext`y, 0, 100}, PlotStyle -> Orange, Lighting -> "Neutral", ClippingStyle -> None, Evaluate[$CellContext`options]]; $CellContext`region3 = Plot3D[50 - 2 ($CellContext`y/3), {$CellContext`x, 0, 100}, {$CellContext`y, 0, 100}, PlotStyle -> Purple, Lighting -> "Neutral", ClippingStyle -> None, Evaluate[$CellContext`options]]; $CellContext`z[ Pattern[$CellContext`t, Blank[]]] := $CellContext`t/3 - 2 ($CellContext`x/3) - $CellContext`y/2; $CellContext`feasibleregion = RegionPlot3D[ And[ 3 $CellContext`x + 5 $CellContext`y + 9 $CellContext`z <= 500, 4 $CellContext`x + 5 $CellContext`z <= 350, 2 $CellContext`y + 3 $CellContext`z <= 150], {$CellContext`x, 0, 100}, {$CellContext`y, 0, 100}, {$CellContext`z, 0, 100}, Mesh -> None, PlotStyle -> Directive[ Opacity[0.5], Red], Evaluate[$CellContext`options]]; Null); Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellID->760663964], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`obj$$ = False, $CellContext`objfunvalue$$ = 230, $CellContext`planes$$ = True, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`planes$$], True, "show planes"}, {True, False}}, {{ Hold[$CellContext`obj$$], False, "hide objective function plane"}, { True, False}}, {{ Hold[$CellContext`objfunvalue$$], 230, "objective function value"}, 80, 240, 10}}, Typeset`size$$ = Automatic, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`planes$252271$$ = False, $CellContext`obj$252272$$ = False, $CellContext`objfunvalue$252273$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`obj$$ = False, $CellContext`objfunvalue$$ = 230, $CellContext`planes$$ = True}, "ControllerVariables" :> { Hold[$CellContext`planes$$, $CellContext`planes$252271$$, False], Hold[$CellContext`obj$$, $CellContext`obj$252272$$, False], Hold[$CellContext`objfunvalue$$, $CellContext`objfunvalue$252273$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> If[$CellContext`planes$$, If[$CellContext`obj$$, Show[$CellContext`region1, $CellContext`region2, \ $CellContext`region3, $CellContext`options], Show[$CellContext`region1, $CellContext`region2, \ $CellContext`region3, Plot3D[ $CellContext`z[$CellContext`objfunvalue$$], {$CellContext`x, 0, 100}, {$CellContext`y, 0, 100}, Mesh -> None, PlotStyle -> Green, ClippingStyle -> None, PerformanceGoal -> "Quality"], $CellContext`options]], If[$CellContext`obj$$, Show[$CellContext`feasibleregion, $CellContext`options], Show[$CellContext`feasibleregion, Plot3D[ $CellContext`z[$CellContext`objfunvalue$$], {$CellContext`x, 0, 100}, {$CellContext`y, 0, 100}, Mesh -> None, PlotStyle -> Green, ClippingStyle -> None], $CellContext`options]]], "Specifications" :> {{{$CellContext`planes$$, True, "show planes"}, { True, False}}, {{$CellContext`obj$$, False, "hide objective function plane"}, { True, False}}, {{$CellContext`objfunvalue$$, 230, "objective function value"}, 80, 240, 10, Appearance -> "Labeled"}}, "Options" :> {}, "DefaultOptions" :> {ControllerLinking -> True}], SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>(($CellContext`options = {AxesLabel -> { Style["x", Italic], Style["y", Italic], Style["z", Italic]}, BoxRatios -> Automatic, SphericalRegion -> True, ViewPoint -> {-0.9, -1.1, 0}, PlotRange -> {{0, 100}, {0, 100}, {0, 100}}, ImageSize -> {450, 400}, PlotRangePadding -> Scaled[0.02]}; $CellContext`region1 = Plot3D[500/9 - $CellContext`x/3 - 5 ($CellContext`y/9), {$CellContext`x, 0, 100}, {$CellContext`y, 0, 100}, PlotStyle -> LightBlue, Lighting -> "Neutral", ClippingStyle -> None, Evaluate[$CellContext`options]]; $CellContext`region2 = Plot3D[70 - 4 ($CellContext`x/5), {$CellContext`x, 0, 100}, {$CellContext`y, 0, 100}, PlotStyle -> Orange, Lighting -> "Neutral", ClippingStyle -> None, Evaluate[$CellContext`options]]; $CellContext`region3 = Plot3D[50 - 2 ($CellContext`y/3), {$CellContext`x, 0, 100}, {$CellContext`y, 0, 100}, PlotStyle -> Purple, Lighting -> "Neutral", ClippingStyle -> None, Evaluate[$CellContext`options]]; $CellContext`z[ Pattern[$CellContext`t, Blank[]]] := $CellContext`t/3 - 2 ($CellContext`x/3) - $CellContext`y/2; $CellContext`feasibleregion = RegionPlot3D[ And[ 3 $CellContext`x + 5 $CellContext`y + 9 $CellContext`z <= 500, 4 $CellContext`x + 5 $CellContext`z <= 350, 2 $CellContext`y + 3 $CellContext`z <= 150], {$CellContext`x, 0, 100}, {$CellContext`y, 0, 100}, {$CellContext`z, 0, 100}, Mesh -> None, PlotStyle -> Directive[ Opacity[0.5], Red], Evaluate[$CellContext`options]]; 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