Question

A company sells two video games, which for convenience we will call A and B. Video game A sells for $60 per cartridge, while video game B sells for $30 per cartridge. Market research shows that if they sell x thousand copies of video game B, then they can sell y thousand copies of video game A, where
y = (40 − 5x)/(10−x)
Approximately how many copies of each video game should they produce to maxi- mize profits? How much profit can they make?

Answer 1

This is clearly a problem in which we need to take the derivative of a function, set the result equal to zero, and solve. But we must first find the function. So we must answer the question, "What are we looking for the maximum of?"

Profit, of course. What is the total profit of this company?