Question

A university is trying to determine what price to charge for tickets to football games. At a price of ​$22 per​ ticket, attendance averages 40,000 people per game. Every decrease of ​$22 adds 10,000 people to the average number. Every person at the game spends an average of ​$3.00 on concessions. What price per ticket should be charged in order to maximize​ revenue? How many people will attend at that​ price?

Answer 1

Thus 40,000 + 2,500 x will attend the game.

Explanation:

We are given that:

• Price of ticket = 22 $
• Average people per game = 40,000
• Addition of people on every decrease = 10,000
• Money spent on game by every person = 3.00 $

Solution:

Now revenue can be calculated as:

Revenue = people x cost of ticket + people x  $6

Revenue = 40,000 x 22 + 40000 x 6

Revenue = 880,000 + 240,000 = 1,120,000 $

Every decrease of $4 adds 10,000 people or

Every decrease of $1 adds 2,500 people

Cost of ticket = $20 - x

Number of people = 40,000 + 2,500 x