After how many hours does she break even?

Question

Mary repairs microwaves. Her revenue is modeled by the function R(h)=20+30h for every h hours she spends repairing microwaves. Her overhead cost is modeled by the function C(h)=10h^2−80 . 

Answer 1

We break even when revenue equals cost

 

30h + 20 = 10h² - 80

 

moving everything to one side to create 

a quadratic we have:

 

10h² - 30h - 100 = 0

Factor out a 10

h² - 3h - 10 = 0

Factors of -10 that add to -3 are (-5)(2)

 

(h-5)(h+2) = 0

 

h = 5 or h = -2

Discarding the negative

We break even at 5 hours

 

Check: 

30h+20=10h²-80

30(5)+20=10(5)²-80

150+20 = 250-80

170 = 170