Posted by **Jane** on Tuesday, February 21, 2012 at 1:39pm.

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 140 shirts in a week at $6 per shirt, but Ep Sig treasurer Julius has solid research indicating that it is possible to sell 350 per week at $3 per shirt.

(a) Based on this information, construct a linear demand equation for Yoda vs. Alien T-shirts, and 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. Find the weekly profit P as a function of the unit price x.

P(x)=

Determine how much the fraternities should charge to obtain the largest possible weekly profit.

x = $___ per T-shirt

What is the largest possible weekly profit?

How do I determine which formula to use and how to solve it?

Thank you.

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