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 sold120shirts in a week at$7per shirt, but Ep Sig treasurer Julius has solid research indicating that it is possible to sell280per week at$3per shirt.

(a) Based on this information, construct a linear demand equatlun 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 $400 for use of the Student Center. Find the weekly profit Pas a function of the unit price x. HINT [See Exampie 4.] PM = Determine how much the fraternities should charge to obtain the largest possible weekly profit. x = $ per T-shlrt What is the largest possible weekly profit"? $