MAT540 Case Analysis

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

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 <= ___

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.

Answer:

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 she make? What factor constrains her from borrowing even more money than this amount (indicated in your answer to the previous question)?

Answer:

After solving the linear program in QM and utilizing the ranging function (see ranging function in QM assessment) the upper bound for food costs is ________.

Since Julia already is starting with $1500 for food cost, she could increase her profit and the most she should borrow from her friend is $_________

If she borrowed money from her friend the additional amount of profit she could generate is _________.

This is determined because when looking in the ranging section of the solution, the dual value is ______. This means it is worth _______ to Julia for each additional dollar that she receives. So with this is mind, we can conclude that …….

The factor that constrains her from borrowing even more money is ….

Conclusion:

C. When Julia looked at the solution in (A), she realized that it would be physically difficult for her to prepare all the hot dogs and barbecue sandwiches indicated in this solution. She believes she can hire a friend of hers to help her for $100 per game. Based on the results in (A) and (B), is this something you think she could reasonably do and should do?

Answer:

In solution A,

In solution B,

Conclusion:

D. Julia seems to be basing her analysis on the assumption that everything will go as she plans. What are some of the uncertain factors in the model that could go wrong and adversely affect Julia’s analysis? Given these uncertainties and the results in (A), (B), and (C), what do you recommend that Julia do?

Answer/Conclusion:

Conclusions/Final thoughts