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Algebra project - produce a rock concert

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Slide1: 

By: Niloy Shah, Asit Shah, and Chris Long

Problem: 

Problem We were hired by Sam to advise him in producing a rock concert. We are to advise Sam on which band, stadium, and ticket price will bring in the most profit. You are assigned to come up with a final conclusion that you will report to me.

Task 1: Revenue Model: 

Task 1: Revenue Model Assume: $20 ticket price Model: R = price x number of tickets sold n= number of tickets sold R = 20n

Task 2: Cost Model: 

Task 2: Cost Model Fixed Costs (F)‏ Costs that stay the same no matter how many tickets are sold. Variable Costs (V)‏ Costs that vary as the number of tickets sold varies.

Task 2 Table: 

Task 2 Table

Task 2: Cost Model cont.: 

Task 2: Cost Model cont. Sample Fixed Cost Models Example 1 - Ms Teak $75,000 - Cotton Bowl $75,000 - Other $55,000 - Total $205,000

Task 2: Cost Model cont.: 

Task 2: Cost Model cont. Example 2 - Dixie Chickens $88,000 - Starplex $60,000 - Other $55,000 - Total $203,000

Task 2: Cost Model cont.: 

Task 2: Cost Model cont. Example 3 - Dixie Chickens $88,000 - Cotton Bowl $75,000 - Other $55,000 - Total $218,000

Task 2: Cost Model cont.: 

Task 2: Cost Model cont. V = Variable Cost m = unit rate n = number of tickets sold C = Cost F = Fixed Cost V = mn C = V + F Therefore C = mn +F

Ms. Teak at Cotton Bowl: 

Ms. Teak at Cotton Bowl

Dixie Chickens at Starplex: 

Dixie Chickens at Starplex

Dixie Chickens at Cotton Bowl: 

Dixie Chickens at Cotton Bowl

Task 3: Profit Model: 

Task 3: Profit Model Scenario: Who’s That at Cotton Bowl $20 ticket price Fixed Costs Cotton Bowl $75,000 Who’s That $48,000 Other Fixed $55,000 Total Fixed $178,000 Variable Cost $4.50 per ticket sold Total Costs c = 4.5n + 178,000 Revenue $20n Breakeven (profit = 0)‏ R = c 20n= 4.5n+ 178,000 15.5n= 178,000

Profit Model of Scenario: 

Profit Model of Scenario

Task 4: Sales Demand: 

Task 4: Sales Demand Ticket sales will diminish as the ticket price increases. This can be modelled with an equation with a negative slope. Example n = number of tickets sold p = price of a ticket n = - 250p + 27740 Example Sales Demand Model ( n = - 250p + 27740)‏

Task 4: Sales Demand cont.: 

Task 4: Sales Demand cont. Sales Demand Model based on the following information: Dixie Chickens at Starplex Amphitheater Sales demand based on following data: $20 ticket price results in sellout of 20,111 tickets $70 ticket price results in sales of 12,800 tickets Can be expressed as ordered pairs (20, 20111) and (70, 12800)‏ slope= -146.22 y =-146.22+ 23,035.4 This can be rewritten to show ticket demand as: n = - 146.22p + 23035.4

Task 4: Sales Demand cont.: 

Task 4: Sales Demand cont. Revenue is a function of ticket sales and ticket price, and ticket sales and variable cost are both a function of ticket price. Revenue with the Sales Demand Model R=pn n=146.22p + 23035.4 therefore: R=p(146.22p + 23035.4) or (146.22p2)+ 23035.4 Variable Cost with sales Demand Model M = unit cost V +mn V =4.5n V= 4.5(146.22p + 23035.4) V = 657.99p+ 103659.3 Total Costs with the Sales Demand Model C = V+F C= (-657.99p + 103659.3) + 203,000 C= 657.99p+ 306659.3 Profit with the Sales Demand Model P= R - C P=(146.22p2 +23035.4p)-(-657.99 + 306659.3)‏ P=146.22p2 + 23693.39p - 306659.3

Slide25: 

Who’s that? at Starplex

Final Recommendation: 

Final Recommendation Who’s that? at Cotton Bowl for $60 a ticket, bringing in a profit of $599,000 © All rights reserved to Explosion Incorporated

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