Question

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.

Answer 1

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.

$20x^2-400=220h-160$

This can simplify to:
$x^2 - 11h - 12 = 0$

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

The only reasonable solution is 12 hours.

Answer 2

The cost and the revenue functions are illustrations of quadratic functions

The company break even after 12 hours

The given parameters are:

Revenue function: R(h) = 220h - 160

Cost function: C(h) = 20h^2 - 400

At break even, both functions are equal.

So, we have:

$20h^2 -400 = 220h- 160$

Rewrite as:

$20h^2 -220h-400 + 160 = 0$

This gives

$20h^2 -220h-240 = 0$

Divide through by 20

$h^2 -11h-12 = 0$

Solve for h

h = -1 or 12

h cannot be negative,

Hence, the company break even after 12 hours

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