Q:

Quick Fix Inc. repairs bikes. The company’s revenue is modeled by the function R(h)=220h−160 for every h hours spent repairing bikes. The company’s overhead cost is modeled by the function C(h)=20h2−400 . After how many hours does the company break even? Enter your answer in the box.

Accepted Solution

A:
The company will break even after 12 hours.

To find this answer, we have to set the equations equal to each other and solve. We will have a quadratic equation.

[tex]20x^2-400=220h-160 [/tex]

This can simplify to:
[tex]x^2 - 11h - 12 = 0[/tex]

The factors of this are: (x - 12) and (x + 1).

The only reasonable solution is 12 hours.