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 400 shirts in a week at $8 per shirt, but Ep Sig treasurer Julius has solid research indicating that it is possible to sell 600 per week at $4 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.
b. The university administration charges the fraternities a weekly fee of $500 for use of the student center. Write down the monthly profit P as a function of the unit price x. Hence, determine how much the fraternities should charge to obtain the largest possible weekly profit. What is the largest possible weekly profit? [HINT: See Example 4.]
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