In[]:=
(*PROBLEMA1*)(*Maximizar:Z=x1+x2Sujetoa:x1-x2>=0×4x1+3x2>=12×9x1+11x2<=99x1<=8x1,x2>=0*)Maximize[{x1+x2,x1-x2>=0&&4x1+3x2>=12&&9x1+11x2<=99&&x1<=8&&x1>=0&&x2>=0},{x1,x2}]​​
Out[]=

115
11
,x18,x2
27
11

In[]:=
(*DefinicióndelasrestriccionesdelProblema1*)region=RegionPlot[x1-x2>=0&&4x1+3x2>=12&&9x1+11x2<=99&&x1<=8&&x1>=0&&x2>=0,{x1,0,10},{x2,0,12},PlotPoints->200,FrameLabel->{"x1","x2"},AxesLabel->{"x1","x2"},PlotStyle->LightBlue,BoundaryStyle->{Thick,Blue},Frame->True,GridLines->Automatic];​​​​(*Resolverelproblemadeoptimización*)​​sol=Maximize[{x1+x2,x1-x2>=0&&4x1+3x2>=12&&9x1+11x2<=99&&x1<=8&&x1>=0&&x2>=0},{x1,x2}]​​​​(*Extraerpuntoóptimo*)​​optPoint={x1,x2}/.sol[[2]];​​​​(*Graficarregiónfactible+puntoóptimo*)​​Show[region,Graphics[{Red,PointSize[Large],Point[optPoint],Text[Style["Óptimo",14,Bold,Red],optPoint+{0.3,0.3}]}]]​​
Out[]=

115
11
,x18,x2
27
11

Out[]=