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

ANSWER

Alan breaks even after 7 hours.

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.