Explanation

(b)
Given constraints are $x \geq 0,\ y \geq 0,\ x + y \leq 5$ and $3x + y \leq 9$ and $z = 12x + 3y$
Here, feasible region id $OABCO$
[image:12_image3.jpeg]
At point $O(0,\ 0),\ z = 12(0) + 3(0) = 0$
At point $A(3,\ 0),z = 12(3) + 3(0) = 36$
At point $B(2,\ 3),\ z = 12(2) + 3(3) = 33$
At point $C(0,\ 5),\ z = 12(0) + 3(5) = 15$
Hence, maximum value is 36