math
posted by John .
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 Tshirts 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 $5 per shirt, but Ep Sig treasurer Julius has solid research indicating that it is possible to sell 480 per week at $2 per shirt.
(a) Based on this information, construct a linear demand equation for Yoda vs. Alien Tshirts, and hence obtain the weekly revenue R as a function of the unit price x.
(b) The university administration charges the fraternities a weekly fee of $500 for use of the Student Center.What is the weekly profit P as a function of the unit price x?
Determine how much the fraternities should charge to obtain the largest possible weekly profit.
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