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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

Alan breaks even after 7 hours.

EXPLANATION

Alan's revenue is modeled by the function

[tex]R(h)=10+30h[/tex]

His overhead cost function is modeled by the function

[tex]C(h)=5 {h}^{2} - 25[/tex]

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

[tex]5 {h}^{2} - 25 = 30h + 10[/tex]

[tex]5 {h}^{2} - 30h - 35 = 0[/tex]

[tex]{h}^{2} - 6h -7 = 0[/tex]

Factorize:

[tex](h - 7)(h + 1) = 0[/tex]

[tex]h = - 1[/tex]

or

[tex]h = 7[/tex]

We discard the negative value.

He breaks even after 7 hours.

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