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This graduate level term paper/case study should be written in APA style, 10 pages and is centered around “The Possibility” Restaurant case studies (included below). While the case study will focus on the mathematical solution, you are also expected to bring value-added material in the way of outside research. The paper should adhere to the following outline.

1. Introduction

a. Start with the problem statements from the two case studies. Don’t simply copy from the text, but briefly restate the problem in your own terms. This should take no more than one page.
b. Provide your value-added material from your research here. You are to research the application of operations research as applied to restaurant operations and provide a brief write-up. The write-up should take at least 3 pages. The material you provide should refer to an area of restaurant operations to which linear programming is applied, such as staff scheduling, food selection and pricing, etc.

2. Solve the problem from the first case study.

a. Formulation of the linear programming problem with each constraint labeled.
b. A graph of the feasible region with each extreme point labeled (X1, X2, Z). You can label the graph directly or provide a separate table of points.

3. Solve the problem from the second case study.
a. A copy and paste of the computer solution.
b. A copy and paste of the sensitivity report.
c. Answer the first question from the last paragraph of the first case study.
d. Answer the second question from the last paragraph of the first case study.
e. Answer question A of the second case study.
f. Answer question B of the second case study.
g. Answer question C of the second case study.

4. Conclusion and Recommendations

a. Recommendations on improvements or changes to the solution model based on your interpretation of the data from the sensitivity report. Examples are, what prices you might charge in keeping with the optimal product mix, the addition of resources to increase profits, etc. I am looking for your value-added input or perspective on this problem.

You may use QM for Windows or Excel to solve your problem. I highly recommend QM for Windows since it will produce a graph of the feasible region for linear programming problems with two decision variables.

If using QM for Windows:
• The computer solution is in the solution window.
• The sensitivity report is in the range window.
• The graph of the feasible region is in the graph window.
• To copy and paste any of these windows, select the window you want to copy and then select Fileà Save As HTML. You can then insert the HTML file into your MS Word document.

If using Excel:
• The computer solution is in the original worksheet.
• The sensitivity report is in its own worksheet.
• There is no graph of the feasible region available. There is freeware and shareware on the internet you can download to produce a graph of the feasible region given the constraint lines you feed it.

To copy and paste the solution and sensitivity report, you highlight the region you wish to copy and select File–>Copy. Then go to your Word document and select Fileà Paste Special, and paste it as a picture. Do not directly copy the cells into the document because you will wind up embedding the MS Excel application into the Word document, causing your file size to increase dramatically..

Case Study #1

Angela Fox and Zooey Caulfield were food and nutrition majors at State University, as well as close friends and roommates. Upon graduation Angela and Zooey decided to open a French restaurant in Draperton, the small town where the university was located. There were no other French restaurants in Draperton and the possibility of doing something new and somewhat risky intrigued the two friends. They purchased an old Victorian home just off Main Street for their new restaurant, which they named “The Possibility.”
Angela and Zooey knew in advance that at least initially they could not offer a full, varied menu of dishes. They had no idea what their local customers’ tastes in French cuisine would be, so they decided to serve only two full-course meals each night, one with beef and the other with fish. Their chef, Pierre, was confident he could make each dish so exciting and unique that two meals would be sufficient, at least until they could assess which menu items were most popular. Pierre indicated that with each meal he could experiment with different appetizers, soups, salads, vegetable dishes, and desserts until they were able to identify a full selection of menu items.
The next problem for Angela and Zooey was to determine how many meals to prepare for each night so they could shop for ingredients and set up the work schedule. They could not afford too much waste. They estimated that they would sell a maximum of 60 meals each night. Each fish dinner, including all accompaniments, requires 15 minutes to prepare, and each beef dinner takes twice as long. There is a total of 20 hours of kitchen staff labor available each day. Angela and Zooey believe that because of the health consciousness of their potential clientele, they will sell at least three fish dinners for every two beef dinners. However, they also believe that at least 10% of their customers will order beef dinners. The profit from each fish dinner will be approximately $12, and the profit from a beef dinner will be about $16.
Formulate a linear programming model for Angela and Zooey that will help them estimate the number of meals they should prepare each night and solve this model graphically.
If Angela and Zooey increased the menu price on the fish dinner so that the profit for both dinners was the same, what effect would that have on their solution? Suppose Angela and Zooey reconsidered the demand for beef dinners and decided that at least 20% of their customers would purchase beef dinners. What effect would this have on their meal preparation meal?

Case Study 2 (“The Possibility” Restaurant cont)

In “The Possibility” Restaurant, Angela and Zooey opened a French restaurant called “The Possibility”. Initially, Angela and Zooey could not offer a full, varied menu, so their chef, Pierre, prepared two full-course dinners with beef and fish each evening. In the case problem, Angela and Zooey wanted to develop a liner programming model to help determine the number of beef and fish meals they should prepare each night. Solve Zooey and Angela’s liner programming model by using the computer.

A. Angela and Zooey are considering investing in some advertising to increase the maximum number of meals they serve. They estimate that if they spend $30 per day on a newspaper ad, it will increase the maximum number of meals they serve per day from 60 to 70. Should they make the investment?
B. Zooey and Angela are concerned about the reliability of some of their kitchen staff. They estimate that on some evenings they could have a staff reduction of as much as 5 hours. How would this affect their profit level?
C. The final question they would like to explore is raising the price of the fish dinner. Angela believes the price for a fish dinner is a little low and that it could be closer to the price of a beef dinner without affecting customer demand. However, Zooey has noted that Pierre has already made plans based on the number of dinners recommended by the linear programming solution. Angela has suggested a price increase that will increase profit for the fish dinner to $14. Would this be acceptable to Pierre, and how much additional profit would be realized?