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 exist30 per ticket, attendance averages 40,000 people per game. Every decrease of exist2 adds 10,000 people to the average number. Every person at the game spends an average of exist5.00 an concessions. What price per decrease of exist2 adds 10,000 people to the average number. Every person at the game spends an average of exist5.00 on concessions. What price per ticket should be charged in order to revenue? How many people will attend at that price? What is the price per ticket? exist

Explanation / Answer

Optimization Problem

At 30 $ , total people= 40000

Total money = 40000*30 = 1200000 $

Let X (X<30) be the Price of ticket, since the question doesn't say about the price increase, we can safely assume price being decreased

No. of people coming to the game for X $ = 40000 + (30-X)*10000/2 ,

Per person spend on concessions = 5

Total price university gets on X$ per ticket = X ( 40000 + (30-X)*10000/2) + 5* (40000 + (30-X)*10000/2)

This equation should be maximized,

= 40000X + 150000X - 5000X2 + 200000+ 7500000 - 25000X

Differentiate wrt x = 40000 + 150000 -10000x + -25000

X= 16.5 $ PER Ticket

No. of People = 40000 + (30-X)*10000/2

= 107500

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