Question

alan repairs televisons. His revenue is modeled by the function r(h)=47+2h 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

3.6 hours

Explanation:

Alan's revenue function is given by:

`r(h) = 47 + 2h`

for every h hours he spends repairing televisions.

His overhead cost is modeled by the function:

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

To find the number of hours Alan breaks even, we need to equate the functions and solve for h.

`47 + 2h = 5 {h}^(2) - 25`

We rewrite in standard form:

`5 {h}^(2) - 2h - 25 - 47 = 0`

This gives:

`5 {h}^(2) - 2h - 72= 0`

Using the quadratic formula:

`h = \frac{ - - 2 \pm \sqrt{( - {2)}^(2) - 4(5)( - 72) } }{2 * 5}`

This gives:

`h = 3.6 \: or \: h = - 4`

Since time is not negative, he breaks even after 3.6 hours.