Booth

Introduction

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 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.

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 this case.

Decision Variables

Representing “x1” as pizza slices, “x2” as hot dogs, and “x3” as barbeque sandwich

The Objective Function

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=$6/8=$0.75

Products |Costs |Sell Prices |Profits | |Pizza |0.75 |1.50 |0.75 | |Hot dog |0.45 |1.50 |1.05 | |Barbeque Sandwich |0.90 |2.25 |1.35 | |

The model is for the first home game,

Maximize Z = $0.75x1 + $1.05x2 + $1.35x3

Where

Z = Total profit

$0.75x1 = profit from pizza

$1.05x2 = profit from hot dog

$1.35x3 = profit from barbeque sandwich

Model Constraints

1. Budget $0.75x1 + $0.45x2 + $0.90x3 = 2.0
5. More than or equal zero X1, X2, X3 >= 0

Graphical Solution of a Maximization Model Maximize Z = $0.75x1 + $1.05x2 + $1.35x3 Subject to: $0.75x1 + $0.45x2 + $0.90x3 = 2.0
X1, X2, X3 >= 0
Solution
[pic]
X1 =