Maximize Revenue from ticket sales word problem

In summary, the problem is to determine the optimal ticket price for a hockey team playing in an arena with a seating capacity of 15,000 spectators. With a ticket price set at $12, the average attendance is 11,000. A market survey suggests that for every dollar the ticket price is lowered, average attendance will increase by 1,000. Using the formula R(x)=xp(x), where p is the demand function, the owners can determine the optimal ticket price to maximize revenue from ticket sales.
  • #1
hvidales
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Homework Statement


Homework Statement [/b]

A hockey team plays in an arena with a seating capacity of 15,000 spectators. With the ticket prices set at $12, average attendance at a game has been 11,000. A market survey indicates that for each dollar the ticket price is lowered, average attendance will increase by 1,000. How should the owners of the team set the ticket price to maximize their revenue from tickets sales?


Homework Equations



R(x)=xp(x) where p is called the demand function(or price function)[x units are sold and the price per unit is p(x)] or P(x) =R(x)-C(x) where x units are sold, C(x) is the cost function and P(x) is the profit.



The Attempt at a Solution


I am stuck on how to set up the problem. I used to R(x)=xp(x) formula and so far I have come up with R(x) = (12-x)(11,000+ 1000x) but I am not sure if that is correct. I was also thinking that this problem is a linear function and perhaps I can some how connect it to the point slope formula and the slope formula. Any help would be nice. Thanks in advance!

 
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  • #2
If the problem were linear, then R(x) would be something like ax, and the optimal solution would be x = 0 or x = infinity.

What you did looks good: if x is the amount the price is lowered, then average attendance is (11000 + 1000x). If you work out the brackets, you will find that R(x) is quadratic, so it will have a clear minimum or maximum.
 

Related to Maximize Revenue from ticket sales word problem

1. What is the best approach to maximize revenue from ticket sales?

The best approach to maximize revenue from ticket sales is to carefully analyze demand and pricing strategies. This includes understanding the target audience, setting competitive prices, and utilizing effective marketing tactics.

2. How can I determine the optimal ticket price for my event?

The optimal ticket price can be determined by conducting market research and analyzing factors such as the cost of production, venue capacity, and competitor pricing. It is also important to consider the perceived value of the event and adjust pricing accordingly.

3. How can I increase ticket sales for my event?

To increase ticket sales, it is important to create a strong promotional campaign and utilize various marketing channels such as social media, email marketing, and partnerships. Offering early bird discounts, group discounts, and other incentives can also help attract more attendees.

4. What role does data analysis play in maximizing revenue from ticket sales?

Data analysis is crucial in identifying trends, understanding customer behavior, and making informed decisions on pricing and marketing strategies. By analyzing data, you can gain insights into which ticket types, pricing strategies, and marketing tactics are most effective in driving revenue.

5. How important is it to have a diverse range of ticket options for an event?

Having a diverse range of ticket options is essential in maximizing revenue from ticket sales. This allows you to cater to different budgets and preferences of potential attendees. It also helps to increase the perceived value of the event and attract a wider audience.

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