Question

Minimise Z=-3x+4y
Subject to x+2y≤8,3x+2y≤12,x≥0,y≥0.

Answer 1

The feasible region determined by the system of constraints,
x+2y≤8, 3x+2y≤12,x≥0 and y≥0 is as follows.

The corner points of the feasible region are O(0,0), A(4,0), B(2,3), and C(0,4).

The value of Z at these corner points are as follows.

Therefore, the minimum value of Z is -12 at the point (4,0).