Raggs, Ltd. a clothing firm, determines that in order to sell x suits, the price
ID: 2860206 • Letter: R
Question
Raggs, Ltd. a clothing firm, determines that in order to sell x suits, the price per suit must be p=1800.5x. It also determines that the total cost of producing x suits is given by Upper C left parenthesis x right parenthesisC(x)=3000+0.75x2. a) Find the total revenue, Upper R left parenthesis x right parenthesisR(x). b) Find the total profit, Upper P left parenthesis x right parenthesisP(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?
Explanation / Answer
a) total revenue = goods sold * price
R = x * (180-0.5 x) = 180 x - 0.5 x^2 ---ANSWER a
b)
Total profit = Cost - Revenue
P = 3000+0.75 x^2 - (180x -0.5x^2)
P = 3000+1.25 x^2 -180 x
c)
to maximimze , find dP/dx = 0
dP/dx = 2.5 * x -180 =0
=> x = 72 -----ANSWER c
d)
maximum profit is when x= 72
P(x) = 3000+1.25 x^2 -180 x
P(72) = 3000+1.25 * 72^2 -180 * 72 = -3480
e)
p = 180 -0.5x = 180 -0.5 * 72 = 144
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