Question

Alan repairs televisions. His revenue is modeled by the function R(h)=10+30h for every h hours he spends repairing televisions. His overhead cost is modeled by the function C(h)=5h^2−25 dollars.

After how many hours does he break even?

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Answer 1

Alan breaks even after 7 hours.

Step-by-step explanation

Alan's revenue is modeled by the function

`R(h)=10+30h`

His overhead cost function is modeled by the function

`C(h)=5 {h}^(2) - 25`

Alan will break even when his cost is equal to his revenue.

`5 {h}^(2) - 25 = 30h + 10`

`5 {h}^(2) - 30h - 35 = 0`

`{h}^(2) - 6h -7 = 0`

Factorize:

`(h - 7)(h + 1) = 0`

`h = - 1`

or

`h = 7`

We discard the negative value.

He breaks even after 7 hours.