Revenue costs

Question

The monthly total for a product is given by R(x) = 300x-0.01x2 dollars, where x is the number of units sold.
(a) To maximize the monthly revenue, how many units must be sold?
(b) What is the maximum possible monthly revenue?

Answer 1

R(x) = -0.01x² + 300x

 

Complete the square

 

R(x) = -0.01(x² - 300000x + 150000²) + 225000000

R(x) = -0.01(x - 150000) + 225000000

 

The maximum revenue, $225,000,000, occurs at 150,000 units.