A factory can produce two products, x and y, with a profit approximated by P = 14x + 22y - 900. The production of y can exceed x by no more than 100 units. Moreover, production levels are limited by the formula x + 2y ≤ 1,400. What production levels yield maximum profit?

Question

Mathematics

Leticia Watts

18 October, 18:44

A factory can produce two products, x and y, with a profit approximated by P = 14x + 22y - 900. The production of y can exceed x by no more than 100 units. Moreover, production levels are limited by the formula x + 2y ≤ 1,400. What production levels yield maximum profit?

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Karen Wade · Answer 1

-x + y < = 100, x + 2y < = 1400. so we have, 3y < = 1500, and so y < = 500. By looking at the Profit equation, we see that the more y and x we have, the more profit we will get, and so, if we set y to it's maximum, which is 500, and set x to maximum which is x = 1400-1000 = 400, then profit will be 14*400 + 22*500 - 900, which is 5600 + 11000 - 900 = 15700