abney

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A man, named Sam, comes to us asking for help in planning a concert, but he’s in it to make the largest amount of money he can. Our job is to figure out which combination of band, stadium, and ticket price can produce the largest profit. We also have to figure out all of the various costs that come with producing a concert, and how that will play out with the final decisions.

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We started by listing all the information and options we had to work with and consider.

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This is where the first chart and graph come into your project. After looking at the information, the one thing left out was tickets. After looking at the situation, we began with the question “How much should be charged for admission?”, excluding details such as band and costs. This is basic. So if we are to assume that tickets are $20 a piece, and if the concert is at the Cotton Bowl, a capacity of 25,704, then your max revenue would be $514,080.

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This is where costs come into play of the production of the concert. In the revenue model, the equation R, revenue, and n, the number of tickets sold, correspond: R=20n. With that revenue, in order to make a profit, you must consider the costs of putting on the show. Your fixed costs, F, is the cost of booking the band, the arena, and other expenses, such as advertising and tickets. And the other main cost is your variable costs. Variable costs depend on the number of people attending, planning things such as security for the certain amount of people. A unit rate can also be found for variable cost, in this case, it is 4.5. The equations below can be found with this information. V= variable cost m= unit rate n= number of tickets sold V=mn C= total cost F= fixed cost P=Profit p=price C= V + F

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Ms Teak at Cotton Bowl

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Dixie Chickens at Cotton Bowl

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Dixie Chickens at Starplex Amphitheatre

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The big day: a base profit is discovered. To do this, we just put together both the revenue and cost models together. An equation can be used to represent this situation as well, P = R – C. P for profit, R for revenue, and C for total cost. Notice there are two lines in the graph. The intersection point, or break-even, is when the revenues and costs are the same. From there, anything on the left of that point is money loss, and anything to the right is money gained, or profit.

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Costs profit Break Even 11,484 tickets!

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In the task, towards the end, something very important is learned. Even though it looks as if as the ticket price increases so does the profit, that is not the case. There is a certain time where if the ticket price goes to high, people will lose interest in the concert and not attend, therefore resulting in loss of money. This is where we must figure out which ticket price will appeal to both the public, and Sam’s bank account. These considerations are modeled as such.

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The final day. Everything comes together. By creating a scatter plot of ticket price and the resulting ticket sales from that of information from a survey for each arena, you can start to figure out all the different profits that you will get with the different combinations of band, arena and ticket price. Once all of that information is put together, you can than find which combination is right for Sam’s situation. Ta-da! Your mathematic model, which grew and grew, and your project for Sam, are complete. That wasn’t so hard, was it?