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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 240 shirts in a week at $6 per shirt, but Ep Sig treasurer Julius has solid research indicating that it is possible to sell 420 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 $100 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)? $

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 240 shirts in a week at $6 per shirt, but Ep Sig treasurer Julius has solid research indicating that it is possible to sell 420 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 $100 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)? $

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
ChapterP: Prerequisites
SectionP.FOM: Focus On Modeling: Making The Best Decisions
Problem 6P
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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 240 shirts in a week at $6 per shirt, but Ep Sig treasurer Julius has solid research indicating that it is possible to sell 420 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 $100 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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