Question

. A factory can produce two products, x and y, with a profit approximated by P = 15x + 20y − 600. The production of y can exceed x by no more than 200 units. Moreover, production levels are limited by the formula x + 2y ≤ 1600 What production levels yield maximum profit?

Answer 1

Maximize
P = 15x + 20y - 600
subject to:
y ≤ x + 200
x + 2y ≤ 1600

From the graphs of y = 200, x + 2y = 1600, y = 0, x = 0.
The corner points are (0, 0), (0, 200), (400, 600), (1600, 0)

Checking the corner points:
For (0, 0): P = 15(0) + 20(0) - 600 = -600
For (0, 200): P = 15(0) + 20(200) - 600 = 4000 - 600 = 3400
For (400, 600): P = 15(400) + 20(600) - 600 = 6000 + 12000 - 600 = 17400
For (1600, 0): P = 15(1600) + 20(0) - 600 = 24000 - 600 = 23400

Therefore, for maximum profit, the factory should produce 1600 units of product x and no prduct y.