Quadratic Functions

Question

A lawn care company charges $20 a week and has 120 clients. The owner estimates that for each $2 increase in its fee, the company would lose 5 clients. What fee should the owner charge to receive the maximum revenue?

Answer 1

Let compony increase fee x-times. We have now: R(x) = (120 - 5x)(20 + 2x) = -10x² + 140x + 2400;

This quadratic function has maximum at vertex, x = - b/2a = - 140/-20 = 7.

So we have fee is 20 + 14 = $34, number of clients 120 - 10 = 110 and maximum revenue max R = 110·34 =

$3740