Question

2. Richmond Appliance repairs washing machines. The revenue that the company earns is given by the function R(h) = 20 + 45h dollars for every h hours spent repairing washing machines. The company’s overhead cost is given by the function C(h) = 5h2 – 30 dollars. For what number of hours does the company break even? Show your work.

Answer 1

The number of hours needed for the company to break even happens when 
$R(h)=C(h)$

$20+45h= 5h^{2}-30$, rearranging to make the equation 'zero' on LHS
$0= 5h^{2}-30-20-45h$
$0= 5h^{2}-45h-50$, divide each term by 5
$0= h^{2}-9h-10$, factorise
$0=(h+1)(h-10)$, equate each factor to zero
$h=-1$ and $h=10$

We choose the positive value of $h$

Hence, the number of hours needed to break even is $h=10$