The maximum value of z = 9x + 13y subject to constraints 2x + 3y ≤...

Given, constraints are$2x + 3y \le 18, 2x + y \le 10, x \ge 0, y \ge 0$.

The feasible region is $OABCO$.

Also, $z = 9x + 13y$

At $O (0,0) , z = 0$

At $A (5,0) , z = 45$

At $B (3,4) , z = 27 + 52 = 79$

At $C (0,6) , z = 78$

$∴$ Maximum value of $z$ is $79$.