The school yearbook costs $15 per book to produce with an overhead of $5500. The yearbook sells for $40. Write a cost and revenue function and determine the break-even point.
Calculate cost function C(b) with b as the number of books:
C(b) = Cost per book * b + Overhead
C(b) = 15b + 5500
Calculate Revenue Function R(b) with b as the number of books:
R(b) = Sales Price per book * b
R(b) = 40b
Calculate break even function E(b):
Break-even Point = Revenue - Cost
Break-even Point = R(b) - C(b)
Break-even Point = 40b - 15b - 5500
Break-even Point = 25b - 5500
Calculate break even point:
Break-even point is where E(b) = 0. So we set 25b - 5500 equal to 0
25b - 5500 = 0
To solve for b, we type this equation into our search engine and we get:
b = 220
Calculate cost function C(b) with b as the number of books:
C(b) = Cost per book * b + Overhead
C(b) = 15b + 5500
Calculate Revenue Function R(b) with b as the number of books:
R(b) = Sales Price per book * b
R(b) = 40b
Calculate break even function E(b):
Break-even Point = Revenue - Cost
Break-even Point = R(b) - C(b)
Break-even Point = 40b - 15b - 5500
Break-even Point = 25b - 5500
Calculate break even point:
Break-even point is where E(b) = 0. So we set 25b - 5500 equal to 0
25b - 5500 = 0
To solve for b, we type this equation into our search engine and we get:
b = 220