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.

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