Consider the system: 2x+y<20 3x+2y<30 x, y>0 Find the vertex points of the system. Then test these vertex points in the objective function, f(z) = 4x + 6y. Find the maximum point.

Question

Consider the system:

2x+y<20

3x+2y<30

x, y>0

Find the vertex points of the system. Then test these vertex points in the objective function, f(z) = 4x + 6y using a graphing calculator. Find the maximum point.

Answer 1

If the constraints on x,y are >or = to zero, the optimal solution is

F(z) =90

x = 0

y = 15

If the constraints must be x,y only > 0, and x & y are non-integer, then the optimal solution would be

x slightly greater than 0.... say .0001

Then y would be 14.9999 etc.

This would make f(z) = 89.9999 approximately