Question

The maximum value of z = 3x + 10y subjected to the conditions 5x + 2y ≤ 10, 3x + 5y ≤ 15, x, y ≥ 0 is ______.

Options

• `510/19`

• 30

• `523/19`

• `532/19`

Answer 1

The maximum value of z = 3x + 10y subjected to the conditions 5x + 2y ≤ 10, 3x + 5y ≤ 15, x, y ≥ 0 is 30.

Explanation:

The feasible region lies on the origin side of 5x + 2y = 10 and 3x + 5y = 15, in first quadrant.

The comer points of the feasible region are O(0, 0), B(0, 3), `"E"(20/19, 45/19)` and C(2, 0)

The maximum value of z = 3x + 10y is at B(0, 3)

∴ Maximum z = 3(0) + 10(3) = 30