To maximize the objective function z = 2x + 3y under the constraints x + y ≤ 30, x - y ≥ 0 , y ≤ 12, x ≤ 20 , y ≥ 3 and x ,y ≥ 0

Question

To maximize the objective function z = 2x + 3y under the constraints x + y ≤ 30, x - y ≥ 0 , y ≤ 12, x ≤ 20 , y ≥ 3 and x ,y ≥ 0  (A) x = 12 , y = 18 (B) x = 18 , y = 12 (C) x = 12 , y = 12 (D) x = 20 , y = 10

Tardigrade Admin · Accepted Answer

The objective function is Maxz = 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).

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

$x = 12, y = 18$

$x = 18, y = 12$

$x = 12, y = 12$

$x = 20, y = 10$

The objective function is Max $z = 2 x + 3 y .$
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).

Q. To maximize the objective function z=2x+3y under the constraints x+y≤30,x−y≥0,y≤12,x≤20,y≥3 and x,y≥0

x=12,y=18

x=18,y=12

x=12,y=12

x=20,y=10