Minimise $Z = 13x - 15y$ subject to the constraints $x + y \le 7$,$2x - 3y + 6 \ge 0$, $x \ge 0$ and $y \ge 0$.

Minimise $Z = 13x - 15y$ subject to the constraints $x + y \le 7,$ $2x - 3y + 6 \ge 0,$ $x \ge 0,$ $y \ge 0$.

Shaded region shown as OABC is bounded and

coordinates of its corner points are (0,0), (7,0),(3,4) and (0,2), respectively.

Hence, the minimum value of Z is (-30) at (0,2).