# Profit maximizing with cost and price functions

I was given the following exercise during an exam:

A company produces two kinds of products with number of x and y pieces. They can sell the first product at a unit price p = 300 - 3x USD and the second one at a unit price q = 325 - 3y USD. The cost is C(x, y) = $x^2 + 5xy + y^2$ USD. How many pieces should be manufactured of each product to maximize the profit? (Find the (only) stationary point of the profit function.)

In theory, the number of first product should be 25, the number of second product should be 20. But I do not really know how they got to that solution.
• Are you sure the numbers in the question are accurate?

• I am 100% sure, I'd send you pictures of the exercise and the supposed correct answer (just the end result), but I cannot.

• The cost function is not correct then.

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