Math problem help?

Question

Athletic Advantage makes athletic shoes for aerobics and running. Their sales manager has determined that their product, P(x), on x pairs of shoes can be found by P(x)= -x^2 + 90x-500. Find the maximum profit that the shoe company can make.

Answer 1

It has to be fewer than 90 pairs because -(90^2) + (90*90) - 500 = -500 (a negative profit).

I think the answer is $1,525 profit if they make 45 pairs of shoes.

Answer 2

Seems to me that the more shoes they make, the more profit they make. So infinity....