Question

To maximize the objective function $z = 2x + 3y$ under the constraints $x + y \leq 30, x - y \geq 0 , y \leq 12, x \leq 20 , y \geq 3$ and $x ,y \geq 0$

• A. $x = 12 , y = 18$
• B. $x = 18 , y = 12$
• C. $x = 12 , y = 12$
• D. $x = 20 , y = 10$

Answer 1

Answer: (B)

$x = 18 , y = 12$

Answer 2

The objective function is Max$z = 2x + 3y .$ The vertices are $A(20, 10), B(18 , 12) , C (12, 12) , D (3, 3)$ and E (20, 3). Hence the maximum value of the objective function will be at (18, 12).