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 $30 per ticket, attendance averages 40,000 people per game. Every decrease of $3 adds 10,000 people to the average number. Every person at the game spends an average of $6.00 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? ___ people Enter your answer in each of the answer boxes.

Explanation / Answer

solution:

Let the price = 30-3x
So number of ticket buyers = 40000 +10000x

Total revenue = (30-3x)(40000+10000x) + 6 (40000 +10000x)

For revenue to be max.

dTR/dx =0
So 10000*(30-3x)+(40000+10000x)*(-6) +6*10000=0
or, 300000-30000x -240000-60000x+60000=0
or, -90000x +120000 =0
So x =12/9=1.33

Price =$(30-3*1.33)=$26
Attendance =40000 +10000*1.33 = 53300

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