Several Homework Problems

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

I need help with several homework problems showing step by step

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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