# Fields Latasha Week8 Assignment 1 Essay

Submitted By llfields
Words: 827
Pages: 4

Quantitative Methods - MAT540

Case Analysis Paper

Julia’s Food Booth
Chapter 3, page 109

Student Name

Date

Professor ____________________
Strayer University

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.)

Maximize Z = 0.75Pizza Slices x1 + _Hot Dogs x2 + _BBQ x3 Food Cost Constraint: _Pizza Slices x1 + _Hot Dogs x2 + _BBQ x3 <= __0.75x1 + 0.45x2 + 0.90x3 <= \$1500.00_

Oven Space Constraint: _Pizza Slices x1 + _Hot Dogs x2 + _BBQ x3 <= 55296

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