The  maximum value of z = 4x + 2y subject to constraints

2x + 3y ≤ 28,

x + y ≤ 10, 

x, y ≥ 0 is :

40

Z = 4x + 2y

x, y ≥ 0  ⇒  solution in 1st quadrant

plotting lines first

2x + 3y = 28

x + y = 10

Checking point O(0, 0)

1. for 2x + 3y ≤ 28

⇒ 0 ≤ 28 (true)

solution lies to side containing (0, 0)

2. x + y ≤ 10

⇒ 0 ≤ 10 (true)

solution lies to side containing (0, 0)