Julia’s Food Booth
Julia Robertson 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 sell.
Most food items
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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.
Linear Programming Model
The following variables were be used: X1 = Slices of Pizza X2 = Hot Dogs X3 = BBQ Sandwiches
The objective is to maximize profit. maximize Z= .75X1+1.05X2+1.35X3
Subject to:
.75X1+1.05X2+1.35X3≤1,500 (Budget)
24X1+16X2+25X3≤55,296in2 (Oven Space)
X1≥X2+X3
X2X3≥2.0
X1, X2, X3≥0
Evaluate the prospect of borrowing money before the first game. | | | | | | | | Adjustable Cells | | | | | | | | | Final | Reduced | Objective | Allowable | Allowable | | Cell | Name | Value | Cost | Coefficient | Increase | Decrease | | $B$12 | Pizza= | 1250 | 0 | 0.75 | 1 | 1.00 | | $B$13 | Hot Dogs= | 1250 | 0 | 1.05 | 1E+30 | 0.27 | | $B$14 | Barbecue= | 0 | 0 | 1.35 | 0.375000011 | 1E+30 | | | | | | | | | Constraints | | | | | | | | | Final | Shadow | Constraint | Allowable | Allowable | | Cell | Name | Value | Price | R.H. Side |
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