Parameters/Background The case study involving Julia’s food booth …. (provide background and parameters very similar to an Executive Summary in a Business Report).
Julia is considering leasing a food booth outside Tech Stadium at home (6) football games.
If she clears $1000 in profit for each game she believes it will be worth leasing the booth.
$1000 per game to lease the booth
$600 to lease a warming oven
She has $1500 to purchase food for first game and will for remaining 5 games she will purchase her ingredients with money made from previous game.
Each pizza costs $6 for 8 slices which is ? per slice, and she will sell it for $1.50
Each hot dog costs 0.45, and she will sell it for $150
Each BBQ Sandwich costs 0.90, and she will sell it for $2.25
There are Food Cost, Oven and Ratio Constraints that include:
QM assessment (Describe the Excel Solver and/or QM for Windows tool input) Pizza Slices x1 Hot Dogs x2 BBQ x3 RHS
Maximize 0.75 0.45x2 0.90x3 <= $1500.00
Food Costs <=
Oven Space <= 55296
Hot Dog to BBQ ratio demand >= 0
Pizza to Hot Dog and BBQ ratio demand >= 0
Equation form (fill in coefficients, amounts, etc.)
Hot Dog to BBZ ratio Constraint: _Hot Dogs x2 + _BBQ x3 >= 0
Pizza to Hot Dog and BBQ Constraint: _Pizza Slices x1 - _Hot Dogs x2 - _BBQ x3 >= 0
Linear Programming Results (from Excel Solver and/or QM for Windows):
Optimal Value (Z) =
Ranging
Case Study Questions
A. Formulate and solve a linear programming model for Julia that will help you advise her if she should lease the booth. x1 – Pizza Slices x2 – Hot Dogs x3 – Barbeque Sandwiches
Subject to:
$0.75x1 + $0.45x2 + $0.90x3 ≤ $1,500
24x1 + 16x2 + 25x3 ≤ 55,296 in2 of oven space x1 ≥ x2 + x3 (changed to –x1 + x2 + x3 ≤ 0 for constraint) x2/x3 ≥ 2 (changed to –x2 +2x3 ≤ 0 for constraint) x1, x2, x3 ≥ 0
Variable | Status | Value |
X1 | Basic | 1250 |
X2 | Basic | 1250 |
X3 | NONBasic | 0 | slack 1 | NONBasic | 0 | slack 2 | Basic | 5296.0 | slack 3 | NONBasic | 0 | slack 4 | Basic | 1250 |
Optimal Value (Z) | | 2250 |
Answer: Yes, Julia would increase her profit ,if she borrowed 158.88 from her friend. The shadow price, or dual value, is $1.50 for each additional dollar that she earns. The upper limit given in the model is $1,658.88, which means that Julia will make a profit of $238.32.
Conclusion: If Julia were to open a food booth at her college’s home football games, her optimal value would be _______with Pizza x1 value _____ Hot dogs x2 value of ____ and BBQ x3 value of ______
B. If Julia were to borrow some more money from a friend before the first game to purchase more ingredients, could she increase her profit? If so, how much should she borrow and how much additional profit would
