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T-Shirt Profit Two fraternities, Sig Ep and Ep Sig, plan to raise money jointly to benefit homeless people on Long Island. They will sell Yoda vs. Alien T-shirts in the student center, but are not sure how much to charge. Sig Ep treasurer Augustus recalls that they once sold 90 shirts in a week at $9 per shirt, but Ep Sig treasurer Julius has solid research indicating that it is possible to sell 630 per week at $3 per shirt. (a) On the basis of this information, construct linear demand equation for Yoda vs. Alien T-shirts. Hence obtain the weekly revenue R as a function of the unit price x. R(x) = (b) The university administration charges the fraternities a weekly fee of $500 for use of the student center. Write down the weekly profit P as a function of the unit price x. P(x) = Determine how much the fraternities should charge (in dollars per T-shirt) to obtain the largest possible weekly profit. x = $ per T-shirt What is the largest possible weekly profit (in dollars)?

T-Shirt Profit Two fraternities, Sig Ep and Ep Sig, plan to raise money jointly to benefit homeless people on Long Island. They will sell Yoda vs. Alien T-shirts in the student center, but are not sure how much to charge. Sig Ep treasurer Augustus recalls that they once sold 90 shirts in a week at $9 per shirt, but Ep Sig treasurer Julius has solid research indicating that it is possible to sell 630 per week at $3 per shirt. (a) On the basis of this information, construct linear demand equation for Yoda vs. Alien T-shirts. Hence obtain the weekly revenue R as a function of the unit price x. R(x) = (b) The university administration charges the fraternities a weekly fee of $500 for use of the student center. Write down the weekly profit P as a function of the unit price x. P(x) = Determine how much the fraternities should charge (in dollars per T-shirt) to obtain the largest possible weekly profit. x = $ per T-shirt What is the largest possible weekly profit (in dollars)?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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T-Shirt Profit Two fraternities, Sig Ep and Ep Sig, plan to raise money jointly to benefit homeless people on Long Island. They will sell Yoda vs. Alien T-shirts in the student center, but are not sure how much to charge. Sig Ep treasurer Augustus recalls that they once sold 90 shirts in a week at $9 per shirt, but Ep Sig treasurer Julius has solid research indicating that it is possible to sell 630 per week at $3 per shirt. (a) On the basis of this information, construct a linear demand equation for Yoda vs. Alien T-shirts. Hence obtain the weekly revenue R as a function of the unit price x. R(x) (b) The university administration charges the fraternities a weekly fee of $500 for use of the student center. Write down the weekly profit P as a function of the unit price x. P(x) = Determine how much the fraternities should charge (in dollars per T-shirt) to obtain the largest possible weekly profit. X = $ per T-shirt What is the largest possible weekly profit (in dollars)? $
Transcribed Image Text:T-Shirt Profit Two fraternities, Sig Ep and Ep Sig, plan to raise money jointly to benefit homeless people on Long Island. They will sell Yoda vs. Alien T-shirts in the student center, but are not sure how much to charge. Sig Ep treasurer Augustus recalls that they once sold 90 shirts in a week at $9 per shirt, but Ep Sig treasurer Julius has solid research indicating that it is possible to sell 630 per week at $3 per shirt. (a) On the basis of this information, construct a linear demand equation for Yoda vs. Alien T-shirts. Hence obtain the weekly revenue R as a function of the unit price x. R(x) (b) The university administration charges the fraternities a weekly fee of $500 for use of the student center. Write down the weekly profit P as a function of the unit price x. P(x) = Determine how much the fraternities should charge (in dollars per T-shirt) to obtain the largest possible weekly profit. X = $ per T-shirt What is the largest possible weekly profit (in dollars)? $
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