Auniversity is trying to determine what price to charge for tickets to football games. at a price of $24 per ticket, attendance averages 40 comma 000 people per game. every decrease of $3 adds 10 comma 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?

 Price per ticket should be charged in order to maximize revenue is $15.

70000 people will attend at this price.

Explanation:

Let 'x' represent the decrease .

Using the given information,

Price per ticket = 24 - 3x

Average no. of people that watch the game = 40000 + 10000x

Additional money spent by every person = 6(40000 + 10000x)

Revenue [R(x)] = Price per ticket Average no. of people that watch the game + Additional money spent

Revenue [R(x)] = (24 - 3x)(40000 + 10000x) + 6(40000 + 10000x)

On solving the above equation we get ,

Revenue [R(x)] = -30000 + 180000x + 1200000

In order to find the critical point we'll differentiate the following with respect to x;

R'(x) = -60000x + 180000

∵ R'(x) = 0  

x = 3

Thus, the price per ticket that should be charged in order to maximize revenue is (24 - 33 = 24 - 9 = $15)

People that will attend at this price = (40000 + 100003) = 70000

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