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)=5h2−25 dollars.

After how many hours does he break even?

Answer 1

After 7 hours, he breaks even.

Explanation:

Break Even Point is when Revenue = Cost.

So we equate the revenue function and cost function, and figure out the value of
`h` to find his break even hours.

`R(h)=C(h)\\10+30h=5h^2-25\\0=5h^2-30h-25-10\\0=5h^2-30h-35\\0=h^2-6h-7\\0=(h-7)(h+1)\\h=7,-1`

The number of hours, h, cannot be negative, so h = 7 is the right answer.

Answer 2

The model that shows the break even point is that which shows that cost is equal to revenue.
10 + 30h = 5h² - 25
The vaue of h is equal to 7. Thus, Alan can only breakeven after 7 hours of working in in the television repair shop.