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 values of Z at these corner points are as follows

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