Maximise the function $Z = 11x + 7y$, subject to the constraints $x \le 3$, $y \le 2,x \ge 0$ and $y \ge 0$.

Maximise $Z = 11x + 7y$, subject to the constraints $x \le 3,y \le 2,x \ge 0,y \ge 0$.

The shaded region as shown in the figure as OABC is bounded

and the coordinates of corner points are (0,0),(3,0),(3,2) and (0,2), respectively.

Hence, Z is maximum at (3,2) and its maximum value is 47 .