# How to make this model in wolfram mathematica?

A model production possibility curve (nonlinear case). I used 1/4 of a circle in the code.

Manipulate[
ParametricPlot[{{12 Cos[t],6 Sin[t]}}, {t,
0, Pi/2},GridLines->Automatic, PlotRange->{{0,15},{0,10}},
AxesOrigin -> {0, 0} ,
LabelStyle -> Directive,
PlotLabel->"Кривая Производственных Возможностей",
AxesLabel->{"товар Х","товар У"},
Epilog -> {PointSize[.05], Point[{{12 Cos[t],6 Sin[t]}}]}], {t,
0, Pi/2}]


I can not make a calculation of points on the curve when driving using the dotted line. Mail can throw off the image of what should be a model. thanks for the help.

Manipulate[ParametricPlot[{{12 Cos[t], 6 Sin[t]}}, {t, 0, Pi/2},
GridLines -> Automatic, PlotRange -> {{0, 15}, {0, 10}},
AxesOrigin -> {0, 0}, LabelStyle -> Directive,
PlotLabel -> "Кривая Производственных Возможностей\n
точка =" <> ToString[{12 Cos[t], 6 Sin[t]}],
AxesLabel -> {"товар Х", "товар У"},
Epilog -> {PointSize[.05], Point[{{12 Cos[t], 6 Sin[t]}}], Red,
Dotted, Line[{{0, 6 Sin[t]}, {15, 6 Sin[t]}}],
Line[{{12 Cos[t], 0}, {12 Cos[t], 10}}]}], {{t, .5}, 0, Pi/2}] • you saved me. thank you very much – Karina Raspberry Jun 12 '16 at 22:30
• @KarinaRaspberry, glad i was able to help. Welcome to mma.se. – kglr Jun 13 '16 at 1:04