Question

Max value of z equals 3x + 2y subject to x + y ≤ 3, x ≤ 2, -2x + y ≤ 1, x ≥ 0, y ≥ 0 is ______ 

Options

• 6

• 8

• 2

• 10

Answer 1

Max value of z equals 3x + 2y subject to x + y ≤ 3, x ≤ 2, -2x + y ≤ 1, x ≥ 0, y ≥ 0 is 8. 

Explanation: 

The feasible region lies on the origin side of all the lines and in the first quadrant.

∴ The corner points of the feasible region are

O (0, 0), A (2, 0), B (2, 1), C`(2/3, 7/3)` and D(0, 1)

Maximum value of z = 3x + 2y is at B (2, 1)

∴ Maximum z = 3 (2) + 2 (1) = 8