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# Julia's Booth Essay

944 words - 4 pages

Julia is a senior at Tech, and she’s investigating different ways to finance her final year at school. She is considering leasing a food booth outside the Tech stadium at home football games. Tech sells out every home game, and Julia knows, from attending the games herself, that everyone eats a lot of food. She has to pay \$1,000 per game for a booth, and the booths are not very large. Vendors can sell either food or drinks on Tech property, but not both. Only the Tech athletic department concession stands can sell both inside the stadium. She thinks slices of cheese pizza, hot dogs, and barbecue sandwiches are the most popular food items among fans and so these are the items she would ...view middle of the document...

Julia has talked to some students and vendors who have sold food at previous football games at Tech as well as at other universities. From this she has discovered that she can expect to sell at least as many slices of pizza as hot dogs and barbecue sandwiches combined. She also anticipates that she will probably sell at least twice as many hot dogs as barbecue sandwiches. She believes that she will sell everything she can stock and develop a customer base for the season if she follows these general guidelines for demand.

If Julia clears at least \$1,000 in profit for each game after paying all her expenses, she believes it will be worth leasing the booth.

A. Formulate a linear programming model for Julia that will help you to advise her if she should lease the booth. Formulate the model for the first home game. Explain how you derived the profit function and constraints and show any calculations that allow you to arrive at those equations.
Let, X1 =No of pizza slices,
X2 =No of hot dogs,
X3 = No of barbeque sandwiches

▪ Objective function co-efficient:
The objective is to maximize total profit. Profit is calculated for each variable by subtracting cost from the selling price.
For Pizza slice, Cost/slice=\$4.5/6=\$0.75
|  |X1 |X2 |X3 |
|SP |\$1.50 |\$1.60 |\$2.25 |
|-Cost |0.75 |\$0.50 |\$1.00 |
|Profit |\$0.75 |\$1.10 |\$1.25 |

Maximize Total profit Z = \$0.75X1 + 1.10X2 +1.25X3

▪ Constraints:

1. Budget constraint:
0.75X1+0.50X2+1.00X3= 2.0 (at least twice as many hot dogs as barbeque sandwiches)
This constraint can be rewritten as:
X2-2X3>=0
X1, X2, X3 >= 0

Model:
Maximize Total profit Z = \$0.75X1 + 1.10X2 +1.25X3
Subject to:
0.75X1+0.50X2+1.00X3=0 (at least twice as many hot dogs as barbeque sandwiches)
X1, X2, X3 >= 0 (Non negativity constraint)

B. Solve the linear programming model using a computer for Julia that will help you advise her if she should lease the booth. In this solution, determine the number of pizza slices, hot dogs and barbecue sandwiches she should sell at each game. Also determine the revenues, cost and profit; and do an analysis of how much money she actually will make each game given the expenses of each game.

Do an analysis of the profit solution and what impact it has on Julia’s ability to have sufficient funds for the next home game to purchase and prepare the food. What would you recommend to Julia?
Following table shows the Excel solver solution for the model:
|Target Cell (Max) | | ...

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