A model for a​ company's revenue from selling a software package is ​R(p)=−2.5p2+650​p, where p is the price in dollars of the software. What price will maximize​ revenue? Find the maximum revenue.

Question

A model for a​ company's revenue from selling a software package is ​R(p)=−2.5p2+650​p, where p is the price in dollars of the software. What price will maximize​ revenue? Find the maximum revenue.

Answer 1

Take the first derivative of the function and set it = 0 to find price for max. profit. (slope of revenue function = 0)

f'(R) = 2(-2.5)p + 650 = 0 -> -5p = -650 -> p = $130 to maximixe revenue.

Rev @ $130 is -2.5(130)² + 650(130) = -42250 + 84500 = $42,250.

As a check, revenue at p = $120 and $140 is $42,000 for both, so $130 is the price for max. revenue.