In a LPP constraints are $3 x+y ≤ 9, x+y ≤ 5, x ≥ 0, y ≥ 0$ and objective function max $(z)=x+2 y$. Maximum value of objective function is:

10

The correct answer is Option (4) → 10

$\text{Constraints: } 3x+y \le 9,\ x+y \le 5,\ x \ge 0,\ y \ge 0$

$\text{Corner points: } (0,0),\ (3,0),\ (0,5),\ (2,3)$

$Z=x+2y$

$Z(0,0)=0$

$Z(3,0)=3$

$Z(0,5)=10$

$Z(2,3)=2+6=8$

$\text{Maximum } Z = 10$

$\text{Maximum value} = 10$