A university is trying to determine what price to charge for tickets to football

Question

A university is trying to determine what price to charge for tickets to football games. At a price of 20 per ticket attendance averages 40,000 people per game. Every decrease of $4 adds 10,000 people to the average number. Every person at the game spends and average of $4 on concessions. What price per ticket should be charged in order to maximize revenue? How many people will attend at that price? What is the price per ticket? What is the average attendance? A university is trying to determine what price to charge for tickets to football games. At a price of 20 per ticket attendance averages 40,000 people per game. Every decrease of $4 adds 10,000 people to the average number. Every person at the game spends and average of $4 on concessions. What price per ticket should be charged in order to maximize revenue? How many people will attend at that price? What is the price per ticket? What is the average attendance? What is the price per ticket? What is the average attendance?

Explanation / Answer

Let the price = 20-4x
hence

number of ticket buyers = 40000 +10000x

Total revenue = (20-4x)*(40000+10000x) + 4* (40000 +10000x)

For revenue to be max, we must have dR/dx =0


So 10000*(20-4x)+(40000+10000x)*(-4) +4*10000=0
or, 200000-40000x -160000-40000x+40000=0
or, -80000x +80000 =0
So x =1

price per ticket =20 -4*1 =$16
average attendance =40000 +10000*1 = 50000

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