Question

?Raggs, Ltd. a clothing? firm, determines that in order to sell x? suits, the price per suit must be p=180?0.75x. It also determines that the total cost of producing x suits is given by C(x)=4000+0.75x^2.

?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 maximize? profit?

Answer 1

Demand is p=180 - 0.75x. Cost function is C(x)=4000+0.75x^2

?a) Find the total? revenue,

R(x)= (PQ) = (180 - 0.75x)x = 180x - 0.75x^2

?b) Find the total? profit,

P(x)= Revenue - cost

= 180x - 0.75x^2 - 4000 - 0.75x^2

= 180x - 1.5x^2 - 4000

?c) How many suits must the company produce and sell in order to maximize? profit?

Keep marginal profit = 0

180 - 3x = 0

x* = 60 suits

?d) What is the maximum? profit?

Profit = 180*60 - 1.5*(60^2) - 4000

= 1400

?e) What price per suit must be charged in order to maximize? profit?

Price = 180 - 0.75*60 = $135 per suit.