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never [62]
3 years ago
11

A university is trying to determine what price to charge for tickets to football games. At a price of ​$24 per​ ticket, attendan

ce 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?
Business
1 answer:
m_a_m_a [10]3 years ago
7 0

Answer:<u><em>  Price per ticket should be charged in order to maximize​ revenue is $15.</em></u>

<u><em>70000 people will attend at this price.</em></u>

<u><em></em></u>

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 \times Average no. of people that watch the game + Additional money spent

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

On solving the above equation we get ,

Revenue [R(x)] = -30000x^{2} + 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

<u><em>Thus, the price per ticket that should be charged in order to maximize​ revenue is (24 - 3\times3 = 24 - 9 = $15)</em></u>

<u><em>People that will attend at this price = (40000 + 10000\times3) = 70000</em></u>

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