with(plots): inequal( { 8*x+2*y<=16, 5*x+2*y<=12,x>=0, y>=0}, x=-1..4, y=-1..8,optionsfeasible=[color="Khaki"]);

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

with(simplex); #Define the objective function and constraints objFn:=4*x[1]+2*x[2]; C:={2*x[1]+x[2]<=6, x[1]+3*x[2]<=9, x[1]>=0, x[2]>=0};

NzFJJmJhc2lzRzYiSStjb252ZXhodWxsR0YkSSZjdGVybUdGJEksZGVmaW5lX3plcm9HRiRJKGRpc3BsYXlHRiRJJWR1YWxHRiRJKWZlYXNpYmxlR0YkSSltYXhpbWl6ZUdJKF9zeXNsaWJHRiRJKW1pbmltaXplR0YsSSZwaXZvdEdGJEkpcGl2b3RlcW5HRiRJKXBpdm90dmFyR0YkSSZyYXRpb0dGJEkmc2V0dXBHRiRJLHN0YW5kYXJkaXplR0Yk

LCYmSSJ4RzYiNiMiIiIiIiUmRiQ2IyIiI0Yr

PCYxIiIhJkkieEc2IjYjIiIiMUYkJkYmNiMiIiMxLCZGJUYpRisiIiQiIioxLCZGJUYtRitGKSIiJw==

#Plot the feasible set inequal(C,x[1]=-1..5,x[2]=-1..5);

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

#Solve: maximize(objFn,C);

PCQvJkkieEc2IjYjIiIiIiIkLyZGJTYjIiIjIiIh

#Reproduce Figure 5, p 65 in the text: with(plots): F1:=3*x[1]+2*x[2]; A:=contourplot(F1,x[1]=-1..60,x[2]=-1..65,contours=[60, 100, 121],linestyle=dot,color=green): C:={(1/40)*x[1]+(1/60)*x[2]<=1,(1/50)*x[1]+(1/50)*x[2]<=1,x[1]>=0,x[2]>=0}; B:=inequal(C,x[1]=-1..60,x[2]=-1..60,optionsfeasible=[color="white"]): display(A,B);

LCYmSSJ4RzYiNiMiIiIiIiQmRiQ2IyIiI0Yr

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