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Algebra -- produce a rock concert project


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Mathematical Modeling:The Diary of Bob: 

Mathematical Modeling: The Diary of Bob By Weston Ruths and David Zhao Group: Bob What? No. I don’t want to buy any cookies. Go away. I got better stuff to do… Like Mathematical Modeling!

Day 1: 

Day 1 My name is Bob. My brother is Sam. Now, Sam is begging me to help with some hillbilly-sounding concert scheme. Being it dat we was both borned from da same momma, me just has to help him.

Day 2: 

Day 2 Now, Sammy just isn’t the brightest guy you’ll ever meet, so I’ve gotta help him. A lot.

Day 3: 

Day 3 And right then, remembering the words of my good old preschool teacher Mr. Simons, I decided to analyze the problem. Basically, we need to find the Ideal.BAND@Ideal.ARENA@Ideal.TICKET.PRICE (man. I can’t believe it…but I miss that guy)

Day 4: 

Day 4 VARIABLES!!! R = Revenue Made C = Total Costs V = Variable Costs F = Fixed Costs n = Number of Tickets Sold p = Price m = Unit Rate P = Profit

Day 4 (continued): 

Day 4 (continued) After a while of contemplating the problem, I drove over to the nursing home and visited Mr. Simons. We had a lengthy discussion over preschool-level mathematics, and then even took a walk in the park. He told me that making a revenue model was the way to go. (I helped him cross the street)

Day 4 (continued): 

Day 4 (continued) Here are the three models Mr. Simons helped me with.

Day 5: 

Day 5 And then, I knew there must be costs involved. In fact, even Mr. Simons agreed with me!!!1 Total Costs = Variable Costs + Fixed Costs Now, variable costs are tricky. They have this thing called unit rate. Unit rate is the cost for each individual concertgoer (to hire concert staff, etc.)

Day 5 (continued): 

Day 5 (continued) Now look at this little table Mr. Simons gave me: As you can see, the unit rate is going to change with the number of people at the concert. And, if you add up the last column, you will come up with each individual concertgoer’s variable cost. ($4.50)

Day 5 (continued): 

Day 5 (continued) Mr. Simons helped me create some equations for the different bands. Ms. Teak@Cotton Bowl: C = 4.5n + 75000 + 75000 Dixie Chickens@Starplex Amphitheater: C = 4.5n + 60000 + 88000 Dixie Chickens@Cotton Bowl: C = 4.5n + 88000 + 75000

Day 5 (continued): 

Day 5 (continued)

Day 5 (continued): 

Day 5 (continued)

Day 5 (continued): 

Day 5 (continued) YEAHHH!!! I’m going to ask Mrs. Simons for a cookie now.

Day 6: 

Day 6 Now life isn’t all about losin’ your $$, so ya gotta use them profit models. Revenue gets to join the fun now! Mr. Simons said to me once, before his hair turned entirely gray, “Profit=Revenue-Cost”. I just had to use my past equations of revenue and cost: R=20n C=4.5n+178,000

Day 6 (continued): 

Day 6 (continued) I made a huge data table.

Day 6 (continued): 

Day 6 (continued) Here are my graphs that went with the data table.

Day 7: 

Day 7 Now that I’ve come such a long way- through cost models, revenue models, and even profit models- it’s time for sales demand. No one wants to pay such huge prices, and Sam isn’t keen on handing out free tickets, so I dialed up Mr. Simons, and he showed me sales demand. (He’s on speed dial, of course)

Day 7 (continued): 

Day 7 (continued) Sales demand has two distinct variables: n, the number of tickets sold p, the price of a ticket We formulated a simply, example model equation: n= -250p+27740 (applies to DixieChickens@TheStarplex)

Day 7 (continued): 

Day 7 (continued) Here is a data table I put together. Here is a graph that goes with the data table.

Day 7 (continued): 

Day 7 (continued) Sales demand by itself is nice, but including how revenue would be affected by it, would be even better! I can now pile all of my tasks into this one ultimate, mega, supremely powerful, master equation! P= -146.22p2 + 23693.39p - 306659.3

Day 7 (continued): 

Day 7 (continued) Here is a graph to go with the ultimate, supremely powerful equation.

Day 8: 

Day 8 Instead of using a example sales demand model, we can now use a real sales demand model with real world stats. I used the Starplex Amphitheater. Here is a graph of the stats (line of best fit included):

Day 8 (continued): 

Day 8 (continued) I used the equation P = pn – 4.5n + F Here is a data table and graph with the projected results:

Day 9: 

Day 9 I now need to stop using silly examples and now use the real stuff. What is the best band? What is the best location? What is the best ticket price? These splendid questions I must answer.

Day 9 (continued): 

Day 9 (continued) Looking at what I know, I know that the bands haven't really affected anything. So I realized that the cheapest band is going to be the best band (which is Who’s That)! How easy was that!? Well, what location would be better? I’m certainly not going to let the cheap band decide…

Day 9 (continued): 

Day 9 (continued) By using the same method I did with the Dixie.Chickens@The.Starplex , I can apply it to Who’s.That@The.Starplex and Who’s.That@The.Cotton.Bowl

Day 9 (continued): 

Day 9 (continued) Here is are data tables and graphs with my results: Who’s That@Starplex

Day 9 (continued) this is a long day….: 

Day 9 (continued) this is a long day…. Who’s That@Cotton Bowl

Day 9 (continued): 

Day 9 (continued) It looks like Cotton Bowl will give us the most money. So in conclusion I think the best combo is: Band: Who’s That Place: Cotton Bowl Ticket Price: $60 Most likely profits: $599,000

Day 9 (continued): 

Day 9 (continued) FINALLY.FINISHED Sammy boy gets the results tomorrow. -- And yep. That was all me. Besides, who needs dumb Mr. Simons anyway?

Day 10: 

Day 10 Houston Chronicle Man Found Dead In Home 2/19/08, Homicide victim Mr. Bob Q. McBobberschnitzel was found dead in his suburban home. Found scattered at the crime scene were an aluminum slope-maker, purple spray-painted TI-83+ calculators, and traces of blue cake frosting. The suspect remains at large.

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