Question

Quick Fix Inc. repairs bikes. The company’s revenue equals R(h) = 400 + 220h dollars for every h hours spent repairing bikes. The company’s overhead cost equals C(h) = 20h2 + 160 dollars.

After how many hours does the company break even?

Answer 1

12 hours

Explanation:

Answer 2

The company will break even when the cost is equal to the revenue.

`C(h)=R(h) \\ 20h^2+160=400+220h \\ 20h^2-220h+160-400=0 \\ 20h^2-220h-240=0 \ \ \ \ \ \ \ \ \ \ \ |/ 20 \\ h^2-11h-12=0 \\ h^2+h-12h-12=0 \\ h(h+1)-12(h+1)=0 \\ (h-12)(h+1)=0 \\ h-12=0 \ \lor \ h+1=0 \\ h=12 \ \lor \ h=-1`

The number of hours must be a positive number, so h=12.

The company breaks even after 12 hours.