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 $100/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 game2 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 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 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 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?

A. Formulate and solve an L.P. model for this case.

1. Decision Variables

X1 = Number of Pizzas Slices

X2 = Number of Hot Dogs

X3 = Number of Hamburgers

2. Objective Function

3. Constraints

The above objective function is subject to the following constraints for operation of the booth for a single game:

Oven Size
First Product Purchase
Required Revenue
Demand for Pizza
Demand for Hot Dogs

Solution

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.

Assignment 1. Linear Programming Case Study

Your instructor will assign a linear programming project for this assignment according to the following specifications.

It will be a problem with at least three (3) constraints and at least two (2) decision variables. The problem will be bounded and feasible. It will also have a single optimum solution (in other words, it won't have alternate optimal solutions). The problem will also include a component that involves sensitivity analysis and the use of the shadow price.

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.