Question

For the function z = 19x + 9y to be maximum under the constraints 2x + 3y ≤ 134, x + 5y ≤ 200, x ≥ 0, y ≥ 0; the values of x and y are ______.

Options

• 10, 38

• 67, 0

• 0, 40

• 30, 34

Answer 1

For the function z = 19x + 9y to be maximum under the constraints 2x + 3y ≤ 134, x + 5y ≤ 200, x ≥ 0, y ≥ 0; the values of x and y are 67, 0.

Explanation:

Feasible region lies on the origin side of 2x + 3y = 134 and x + 5y = 200, in first quadrant.

The comer points of the feasible region are

O(0, 0), A(67, 0), B(10, 38) and C(0, 40)

At A (67, 0), z = 1273

At A (10, 38), z = 532

At A (0, 40), z = 360

∴ Maximum value of z is at B (67, 0)