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?
Break even is where R = C
So we have
10 + 30 h = 5h^2 - 25 simplify
5h^2 - 30h - 35 = 0 divide through by 5
h^2 - 6h - 7 = 0 factor
(h - 7) ( h + 1) = 0
Set both factors = 0 and solve for h and we get that
h = 7 or h = -1
Only the first makes sense...so....Alan breaks even after 7 hours