Math: Differential Calculus (Freshman College Course)?

Question

A company manufacturing lawn-mowers
finds that its weekly cost and demand equations are

C(x) = 80 + 24x; p(x) = 60 - x/6

when it sells x lawn-mowers per week. If
the company can sell all the lawn-mowers it
manufactures, determine the maximum profit
from the sale of these lawn-mowers.

1. maximum profit = $1854
2. maximum profit = $1864
3. maximum profit = $1859
4. maximum profit = $1874
5. maximum profit = $1869

Answer 1

If the unit price is p(x), and x lawnmowers are sold, then the revenue R is given by

R(x) = x*p(x) = 60x - x²/6

Profit is Revenue minus Cost:

P(x) = R(x) - C(x) = 60x - x²/6 - (80 + 24x) = -x²/6 + 36x - 80

Maximize P. You should get maximum profit = $1864