Raggs, Ltd., a clothing firm, determines that in order to sell x suits, the price per suit must be
p(x) = 150 − 0.5x.
It also determines that the total cost of producing x suits is given by
C(x) = 4000 + 0.25x2.
(a) Find the total revenue R(x) and the total profit P (x).
(b) How many suits must the company produce and sell in order to maximize profit?
(Verify that it is indeed a maximum!)
(c) What price per suit must be charged in order to maximize profit?

Question

Raggs, Ltd., a clothing firm, determines that in order to sell x suits, the price per suit must be
p(x) = 150 − 0.5x. 
It also determines that the total cost of producing x suits is given by
C(x) = 4000 + 0.25x2. 
	(a) Find the total revenue R(x) and the total profit P (x).
	(b) How many suits must the company produce and sell in order to maximize profit?
(Verify that it is indeed a maximum!)
	(c) What price per suit must be charged in order to maximize profit?