A company makes toy boats. Their monthly fixed costs are $1500. The variable costs are $50 per boat. They sell boats for $75 a piece. How many boats must be sold each month to break even?
Set up Cost function C(b) where t is the number of tapestries:
C(b) = Cost per boat * number of boats + Fixed Cost
C(b) = 50b + 1500
Set up Revenue function R(b) where t is the number of tapestries:
R(b) = Sale Price * number of boats
R(b) = 75b
Break even is where Revenue equals Cost, or Revenue minus Cost is 0, so we have:
R(b) - C(b) = 0
75b - (50b + 1500) = 0
75b - 50b - 1500 = 0
25b - 1500 = 0
To solve for b, we type this equation in our math engine and we get:
b = 60
Set up Cost function C(b) where t is the number of tapestries:
C(b) = Cost per boat * number of boats + Fixed Cost
C(b) = 50b + 1500
Set up Revenue function R(b) where t is the number of tapestries:
R(b) = Sale Price * number of boats
R(b) = 75b
Break even is where Revenue equals Cost, or Revenue minus Cost is 0, so we have:
R(b) - C(b) = 0
75b - (50b + 1500) = 0
75b - 50b - 1500 = 0
25b - 1500 = 0
To solve for b, we type this equation in our math engine and we get:
b = 60