Week 7, Assignment 3

Quantitative Methods - MAT540
Case Analysis Paper
Julia’s Food Booth
Chapter 3, page 109
Professor Azad
February 21, 2013

The case study involving Julia’s food booth, Julia is a senior at a University who is thinking about financing her final year at college, she is considering to open a food booth at the schools stadium, whenever there is a home football game. Julia negotiated with a local pizza delivery company to deliver pizza prior to the game, and she planning on making barbecue sandwich herself the night before the game, she is also planning on selling hot dog, the cost of the food are a piece of pizza for $1.50 and a hot dog for $1.60 each and a barbecue sandwich for $2.25. She has $1,500 in cash available to purchase and prepare the food items for the first home game; for the remaining five games she will purchase her ingredients with money she has made from the previous game. As long as Julia is able to earn a profit of $1000 per game, she will consider her business venture successful.

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|Constraints: | | | |Available |Usage |Left over |
|Budget ($) |0.75 |0.45 |0.90 | 1,500 | 1,500.00 |0 |
|Oven space (sq. in.) |24 |16 |25 | 55,296 | 50,000.00 |5296 |
|Demand |1 |-1 |-1 |0 | - |0 |
|Demand |0 |1 |-2 |0 | 1,250.00 |-1250 |
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|Cost |0.75x1 + 1.05x2 + 1.35x3 ≤ 1500 | | | | |
|Space |24x1 + 16x2 +25x3 ≤ 55296 | | | | |
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She can sell at least as many pizzas as hotdogs and BBQ sandwiches: X1>=X2+X3
She can sell twice as many hotdogs as BBQ sandwiches: X2/X3>=2, X2-2X3>=0
X1, X2, X3 >=0
|Space required for pizza: 14 x 14 = 196 sq inches |
|Space required for each pizza slice: 196/8 = 24.5 sq inches |
|The total space available is the dimension of a shelf, 36 in. * 48 in. = 1,728 inches squared, multiplied |
|By 16 shelves, 27,648 inches squared, which is multiplied by 2, the times before kickoff and halftime the oven will be filled = 55,296 in2. |
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