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Algebra project - produce a rock concert

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-Sam Arteste, a concert producer, has asked us for some help -He is interested in knowing what band, location, and price of ticket he should choose to bring in the most profit. -He has provided us with the three bands and two locations he has narrowed down to. He has also provided us with other important information, such as payment of workers -Our job is to find how Sam can earn the most profit, and show the steps of how we approached there.

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n=number of tickets p= price c= cost FC= fixed cost P= profit R= revenue M= unit rate V=variable cost Throughout this project, there are several variables used. We have defined these variables above. Copyright © 2008. Elements Inc. Mehta, Pham, Shah.

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Revenue- Amount earned without subtracting the cost. Cost- Amount that you must pay off. (Subtract from amount earned) Profit- Amount of money “you pocket”. (The revenue minus cost) Break-even Point- The point where revenue and cost are equivalent. There is no profit. Copyright © 2008. Elements Inc. Mehta, Pham, Shah.

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Certain Costs (such as payment of workers) vary depending on the number of people who attend. Finding the unit rate allows us to then create a cost model. Copyright © 2008. Elements Inc. Mehta, Pham, Shah. C=4.5n+fixed cost

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Copyright © 2008. Elements Inc. Mehta, Pham, Shah. We were provided with a data table that shows the estimated ticket sales at different prices. As you can see, the relationship between the ticket sales and price is not linear. Therefore, we are required to create a scatter plot to find a line of best fit.

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Copyright © 2008. Elements Inc. Mehta, Pham, Shah. Using the information from the data table, we were able to create a scatter plot and find a line of best fit. The equations for each line are stated under each graph. These equations help us find the profit for each combination.

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Copyright © 2008. Elements Inc. Mehta, Pham, Shah. For this scenario, the quadratic equations are created in the following manner: Profit= Revenue-Cost P= (Ticket Price x Tickets Sold)- (Fixed cost+ Variable cost) P= p x n – (FC+ Variable Unit Cost x Tickets Sold) P= p x n – (FC+U x n) P= p x (-146.43p+21429) – [FC+4.5(-146.43p+21429)] In this example, we will use information from Dixie Chickens performing at Starplex. P= p x (-146.43p+21429) – [203000+4.5(-146.43p+21429)] P= -146.43p^2+21429 – 203000+658.935p-21429 P= -146.43p^2+658.935p-203000 This same procedure is used to find the quadratic equations for each combination.

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Copyright © 2008. Elements Inc. Mehta, Pham, Shah. In addition to creating six quadratic equations and graphing them, we made one big data table showing the different profits for each of the six combinations. This showed us the exact dollar values of profit. The values highlighted in purple are the maximum profit of that particular band and location Values in parenthesis show loss (negative profit)

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You need to book “Who’s That?” at the Cotton Bowl, and charge $60 per ticket!

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Incase you were curious about the number of people the concert would bring in, here is what we found out: We found it surprising and interesting that the concert did not have to be a sell-out. In fact, during the “Who’s That” performance at the concert (the combination with the most profit), the stadium was only approximately half full, with 13,678 out of 25,704 available seats full. So, to make the most profit, the concert did not have to be a sell-out! This is a very important aspect that people that produce concerts must take under note. Copyright © 2008. Elements Inc. Mehta, Pham, Shah.