Question

The minimum value of z = 7x + 9y subject to 3x + y ≤ 6, 5x + 8y ≤ 40, x ≥ 0, y ≥ 2 is ______.

Options

• 45

• 18

• 9

• `82/3`

Answer 1

The minimum value of z = 7x + 9y subject to 3x + y ≤ 6, 5x + 8y ≤ 40, x ≥ 0, y ≥ 2 is 18.

Explanation:

Feasible region lies on origin side of lines 3x + y = 6 and 5x + 8y = 40 and above line y = 2, in first quadrant.

The corner points of the feasible region

`"A"(0, 2), "B"(4/3, 2), "C"(8/19, 90/19)` and D(0, 5)

At A(0, 2), z = 18

At `"B"(4/3, 2)`, z = `82/3`

At c = `(8/19, 9/19)`, z = `866/19`

At D(0, 5), z = 45

∴ Minimum value of z is 18.