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 240 shirts in a week at $5 per shirt, but Ep Sig treasurer Julius has solid research indicating that it is possible to sell 400 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.
b. The university administration charges the fraternities a weekly fee of $500 for use of the Student Center. Write down the monthly profit P as a function of the unit price x, and hence determine how much the fraternities should charge to obtain the largest possible weekly profit. 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.

b. The university administration charges the fraternities a weekly fee of $500 for use of the Student Center. Write down the monthly profit P as a function of the unit price x, and hence determine how much the fraternities should charge to obtain the largest possible weekly profit. What is the largest possible weekly profit?

Step-by-step explanation:

first, we must determine the slope = (400 - 240) / (3 - 5) = 160 / -2 = -80

the demand equation:

y - 240 = -80 (x - 5)

y = -80x + 400 + 240

y = 640 - 80x

total weekly revenue:

xy = -80x² + 640x

xy - 500 = -80x² + 640x - 500

max. profit ⇒ x = -640 / (2 x -80) = -640 / -160 = 4

maximum weekly profit = -80($4²) + 640($4) - $500 = -$1,280 + $2,560 - $500 = $780

any options?

step-by-step explanation:

60: 45 =12: 9 =4: 3 so the answer is 4: 3