Question:
Maximise $Z=3 x+2 y$
subject to $x+2 y \leq 10,3 x+y \leq 15, x, y \geq 0$.
Solution:
The feasible region determined by the constraints, $x+2 y \leq 10,3 x+y \leq 15, x \geq 0$, and $y \geq 0$, is as follows.
The corner points of the feasible region are A (5, 0), B (4, 3), and C (0, 5).
The values of Z at these corner points are as follows.
Therefore, the maximum value of Z is 18 at the point (4, 3).