Strayer Course MAT 540 Week 8 Case

MAT 540 Assignment 1

Shannon’s Food Booth

Complete "Shannon's Food Booth" case problem. Address each of the issues A - D according the instructions given. • (A) Formulate and solve an L.P. model for this case. • (B) Evaluate the prospect of borrowing money before the first game. • (C) Evaluate the prospect of paying a friend $150/game to assist. • (D) Analyze the impact of uncertainties on the model.

Shannon Smith 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 Shannon knows, from attending the games herself, that everyone eats a lot of food. She has to pay $1,250 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 hamburgers are the most popular food items among fans and so these are the items she would sell. Most food items are sold during the hour before the game starts and during half time; thus it will not be possible for Shannon to prepare the food while she is selling it. She must prepare the food ahead of time and then store it in a warming oven. For $900 she can lease a warming oven for the six-game home season. The oven has 16 shelves, and each shelf is 3 feet by 4 feet. She plans to fill the oven with the three food items before the game and then again before half time. Shannon has negotiated with a local pizza delivery company to deliver 14-inch cheese pizzas twice each game 2 hours before the game and right after the opening kickoff. Each pizza will cost her $4 and will include 8 slices. She estimates it will cost her $0.35 for each hot dog and $0.75 for each hamburger if she makes the hamburger herself the night before. She measured a hot dog and found it takes up about 16 square inches of space, whereas a hamburger takes up about 25 square inches. She plans to sell a slice of pizza for $1.25, a hot dog for $1.50 apiece and a hamburger for $3.00. She has $1,000 in cash available to purchase and prepare the food items for the first home game; for the remaining five games she will purchase her ingredients with money she has made from the previous game. Shannon has talked to some students and vendors who have sold food at previous football games at Tech as well as at other universities. From this she has discovered that she can expect to sell at least as many slices of pizza as hot dogs and hamburgers combined. She also anticipates that she will probably sell at least twice as many hot dogs as hamburgers. 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 Shannon clears at least $750 in profit for each game after paying all her expenses, she believes it will be worth leasing the booth. A. Formulate and solve a linear programming model for Shannon that will help you advise her if she should lease the booth. B. If Shannon 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

MAT 540 Assignment 1

borrowing even more money than this amount (indicated in your answer to the previous question)? C. When Shannon looked at the solution in (A), she realized that it would be physically difficult for her to prepare all the hot dogs and hamburgers indicated in this solution. She believes she can hire a friend of hers to help her for $150 per game. Based on the results in (A) and (B), is this some- thing you think she could reasonably do and should do? D. Shannon 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 Shannon’s analysis? Given these uncertainties and the results in (A), (B), and (C), what do you recommend that Shannon do?

The assignment will be graded using the associated rubric. Points: 110 Assignment 1: Linear Programming Case Study Criteria Unacceptable Below 60% F Meets Minimum Expectations 60-69% D Fair 70-79% C Proficient 80-89% B Exemplary 90-100% A

Explain what type of problem this is and the approach you are taking (20%)

Did not explain what type of problem this is and the approach taken, or did so insufficiently.

Insufficiently explained what type of problem this is and the approach taken

Partially explained what type of problem this is and the approach taken

Satisfactorily explained what type of problem this is and the approach taken

Thoroughly explained what type of problem this is and the approach taken

Objective function specified correctly in writeup (10%)

Objective function is specified incorrectly, with both coefficients incorrect or missing.

Objective function is specified, but one (1) coefficient is incorrect.

Coefficients for objective function are correct, but whether this is a max or min problem is incorrect.

Objective function is specified correctly.

Constraints are specified correctly in writeup (10%)

Constraints are specified incorrectly or missing.

Some constraints are correctly specified.

Most constraints are correctly specified.

All constraints are correctly specified, buy applicable nonnegativity constraints are omitted.

All constraints are correctly specified, including nonnegativity constraints, if applicable.

Specified L.P. Model is correctly translated to Excel (10%)

Specified L.P. Model is incorrectly translated into Excel

Specified model is translated to Excel in a partially correct manner

Specified model is translated to Excel in a mostly correct manner

Specified model is correctly translated to Excel

Correct Answer is Obtained (10%)

Correct optimum is not obtained

Correct optimum is obtained

Correctly answer the sensitivity analysis

Did not attempt the sensitivity analysis part of

Insufficiently explained and/or provided

Partially explained and/or provided a partially correct

Satisfactorily explained and correctly

Thoroughly explained and correctly

MAT 540 Assignment 1

part of the problem. (15%)

the problem or did so with less than 60% accuracy and completeness

a partially correct answer to the sensitivity analysis part of the problem

answer to the sensitivity analysis part of the problem

answered the sensitivity analysis part of the problem

answered the sensitivity analysis part of the problem

Correctly answer the shadow price part of the problem. (15%)

Did not attempt the sensitivity analysis part of the problem or did so with less than 60% accuracy and completeness

Insufficiently explained and/or provided a partially correct answer to the sensitivity analysis part of the problem

Partially explained and/or provided a partially correct answer to the sensitivity analysis part of the problem

Satisfactorily explained and correctly answered the sensitivity analysis part of the problem

Thoroughly explained and correctly answered the sensitivity analysis part of the problem

5. Writing / Grammar and mechanics

(10%)

Serious and persistent errors in grammar, spelling, and punctuation.

Numerous errors in grammar, spelling, and punctuation.

Partially free of errors in grammar, spelling, and punctuation.

Mostly free of errors in grammar, spelling, and punctuation.

Free of errors in grammar, spelling, and punctuation.

Hints

Data Provided

Shannon’s food booth includes the following costs:

Booth Rental: $1,250 per game

Oven: $900 for 6 games / $150 per game

Profit Goal: $750 per game Item Marginal Cost ($) Marginal Revenue ($) Marginal Profit ($) Size (sq in)

Pizza Slices

.50

1.25

0.75

19.23

Hot Dog

.35

1.50

1.15

16

Hamburger

.75

3.00

2.25

25

• Oven Size

The oven has sixteen (16) racks. Each rack is 3’ x 4’. The oven is filled twice, once before the game and once at halftime.

Oven space = 3 feet (36 inches) x 4 feet (48 inches) x 16 shelves x 2 times per game

36x48x16x2 = 55,296 sq inches

Area = 3.14 x (7 inches) squared or

153.86 sq inches/8 slices or 19.23 square inches per slice