Statistics Home Work

additional_week_8_assignment_1.docx

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MAT540 Week 8 Assignment:

Case Problem Julia’s Food Booth

Julia Robertson 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 to pay $1,000 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 barbecue sandwiches 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 Julia 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 $600 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.

Julia 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 $6 and will include 8 slices. She estimates it will cost her $0.45 for each hot dog and $0.90 for each barbecue sandwich if she makes the barbecue herself the night before. She measured a hot dog and found it takes up about 16 square inches of space, whereas a barbecue sandwich takes up about 25 square inches. She plans to sell a slice of pizza and a hot dog for $1.50 apiece and a barbecue sandwich for $2.25. She has $1,500 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.

Julia 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 barbecue sandwiches combined. She also anticipates that she will probably sell at least twice as many hot dogs as barbecue sandwiches. 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 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.

Since this case has been used before, we will change some of the inputs

# of shelves in the oven: 18 (instead of 16 as in the book)

Cash available: $1800 (instead of 1500 as in the book)

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 $100/game to assist.

· (D) Analyze the impact of uncertainties on the model.

Please read the instructions for the assignment and the rubric on the course guide very carefully.

Here are the instructions for this assignment:

You will be turning in two (2) deliverables, a short writeup of the project and the spreadsheet showing your work.

Writeup.

Your writeup should introduce your solution to the project by describing the problem. Correctly identify what type of problem this is. For example, you should note if the problem is a maximization or minimization problem, as well as identify the resources that constrain the solution. Identify each variable and explain the criteria involved in setting up the model. This should be encapsulated in one (1) or two (2) succinct paragraphs.

After the introductory paragraph, write out the L.P. model for the problem. Include the objective function and all constraints, including any non-negativity constraints. Then, you should present the optimal solution, based on your work in Excel. Explain what the results mean.

Finally, write a paragraph addressing the part of the problem pertaining to sensitivity analysis and shadow price.

Excel.

As previously noted, please set up your problem in Excel and find the solution using Solver. Clearly label the cells in your spreadsheet. You will turn in the entire spreadsheet, showing the setup of the model, and the results.

Your work will be graded according to the following 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 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
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.