How to find the maximum revenue from a word problem.

Question

A model for a company's revenue from selling a software package is R(p)=-2.5p^2+550 p, where p is the price in dollars of the software. What price will maximize revenue? Find the maximum revenue.

Answer 1

R(p) = -2.5p² + 550p

 

The graph of f(x) = Ax² + Bx + C (A≠0) is a parabola.  When A < 0, the graph has maximum value when x = -B/(2A).

 

So, R(p) has maximum value when p = -550/(2(-2.5)) = $110

 

Maximum revenue = R(110) = -2.5(110)² + 550(110) = $30,250