A clothing firm determines that in order to sell x suits, the price per suit must be p = 150 - 0.5x. It also determines that the total cost of producing x suits is given by C(x) = 4000 + 0.25x^2.

Question

a. Find the total revenue R(x).
b. Find the total profit P(x).
c. How many suits must the company produce and sell in order to maximize profit?
d. What is the maximum profit?
e. What price per suit must be charged in order to make this maximum profit?

Answer 1

Okay...

x=the number of suits sold
price=150-0.5x
cost=C(x)=4000+0.25x^2

a) Revenue is the total money made which is just the price times the number of suits sold, hence:
R(x)=(150-0.5x)(x)

b) Profit is the amount of money made or revenue minus the cost, hence:
P(x)=R(x)-C(x)