A company’s profit in dollars is modeled by the equation p(x) = –0.5x2 + 100x, where x represents the number of units sold.

Question

1. How many units does the company need to sell to reach the maximum profit?
2. What's the company’s maximum profit?

Answer 1

The maximum will occur when the derivative of profit with respect to sales is zero.

dP/dx = -x + 100 = 0

You solve that one!

Then take the value of x and plug it into P(x) to get the maximum Profit.