Question

Minimise Z = −3x + 4y

subject to.

Answer 1

The feasible region determined by the system of constraints, 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.

Corner point	Z = −3x + 4y
0(0, 0)	0
A(4, 0)	−12	→ Minimum
B(2, 3)	6
C(0, 4)	16

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