A book publishing company has fixed costs of $180,000 and a variable cost of $25 per book. The books they make sell for $40 each.
Set up Cost Function C(b) where b is the number of books:
C(b) = Fixed Cost + Variable Cost x Number of Units
C(b) = 180,000 + 25(b)
Set up Revenue Function R(b):
R(b) = 40b
Set them equal to each other
180,000 + 25b = 40b
Subtract 25b from each side:
15b = 180,000
Divide each side by 15
b = 12,000 for break even
Set up Cost Function C(b) where b is the number of books:
C(b) = Fixed Cost + Variable Cost x Number of Units
C(b) = 180,000 + 25(b)
Set up Revenue Function R(b):
R(b) = 40b
Set them equal to each other
180,000 + 25b = 40b
Subtract 25b from each side:
15b = 180,000
Divide each side by 15
b = 12,000 for break even