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) = 5000 + 0.5x². 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?
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) = 5000 + 0.5x². 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?
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter8: Functions
Section8.CR: Review Problem Set
Problem 50CR
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Transcribed Image Text: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) = 5000 + 0.5x².
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?
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VIEWStep 2: Find the total revenue function.
VIEWStep 3: Find the total profit function.
VIEWStep 4: Determine the number of suits to maximize the profit.
VIEWStep 5: Find the maximum profit.
VIEWStep 6: Find the price per suit that must be charged in order to maximize profit.
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