Question:
Minimise Z = −3x + 4y
subject to $x+2 y \leq 8,3 x+2 y \leq 12, x \geq 0, y \geq 0$.
Solution:
The feasible region determined by the system of constraints, $x+2 y \leq 8,3 x+2 y \leq 12, x \geq 0$, and $y \geq 0$, 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).
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