Question

A furniture manufacturer must pay $16.91 to make a certain kind of chair, which it can sell for $55.75. If the manufacturer has starting overhead costs of $18,340, not including production costs, how many chairs must it sell to realize a profit of $24,850, to the nearest chair?
a.
1,112
b.
918
c.
775
d.
640

Answer 1

Let n = number of chairs. Profit = revenue − total cost = 55.75n − (18,340 + 16.91n) = (55.75 − 16.91)n − 18,340 = 38.84n − 18,340.

Set equal to desired profit 24,850:
38.84n − 18,340 = 24,850
38.84n = 43,190
n = 43,190 / 38.84 ≈ 1,111.998 ≈ 1,112 chairs.

Answer: a. 1,112