### Several Homework Problems

I’m trying to study for my Calculus course and I need some help to understand this question.

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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 210 shirts in a week at \$5 per shirt, but Ep Sig treasurer Julius has solid research indicating that it is possible to sell 420 per week at \$2 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.

 R(x) =

(b) The university administration charges the fraternities a weekly fee of \$300 for use of the student center. Write down 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?
\$

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