At a large institution of higher learning, the demand for football tickets at each game is 100,000 - 6,000p.If the capacity of the stadium at that university is 60,000 seats, what is the revenue maximizing price for this university to charge per ticket?
A)$16.67
B)$8.33
C)$6.67
D)$4.17
E)$25

Question

Quizplus · Accepted Answer

Since the demand for football tickets is 100,000 − 6,000p, the revenue generated will be the product of the quantity sold and the price:

Revenue = Quantity Sold × Price
Revenue = (60,000) × (100,000 − 6,000p)
Revenue = 6,000,000,000 − 360,000,000p

To find the revenue maximizing price, we need to differentiate revenue with respect to price and set it equal to zero:

d(Revenue)/dp = -360,000,000 = 0
p = $8.33

Therefore, the university should charge $8.33 per ticket to maximize revenue.

At a Large Institution of Higher Learning, the Demand for Football