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

, rearranging to make the equation 'zero' on LHS

, divide each term by 5

, factorise

, equate each factor to zero

and

We choose the positive value of

Hence, the number of hours needed to break even is

Explanation:

Answer 2

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`