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 80 shirts in a week at $8 per shirt, but Ep Sig treasurer Julius has solid research indicating that it is possible to sell 280 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.
q(x) =
R(x) =
(b) The university administration charges the fraternities a weekly fee of $200 for use of the Student Center. Enter 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.
$ ______ per T-shirt
What is the largest possible weekly profit?
$ ______
(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.
q(x) =
R(x) =
(b) The university administration charges the fraternities a weekly fee of $200 for use of the Student Center. Enter 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.
$ ______ per T-shirt
What is the largest possible weekly profit?
$ ______