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 70 shirts in a week at $9 per shirt, but Ep Sig treasurer Julius has solid research indicating that it is possible to sell 420 per week at $4 per shirt.

Question

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 70 shirts in a week at $9 per shirt, but Ep Sig treasurer Julius has solid research indicating that it is possible to sell 420 per week at $4 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 $200 for use of the Student Center. Find the weekly profit P as a function of the unit price x. HINT [See Example 4.]

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?
$