# Mat/540 week 8 assignment 1 linear programming case study

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.

The Rayhoon Restaurant:
Brayden and Behrad were roommates. They decided to open a restaurant in the small town that they were living. They bought an old home for their new restaurant which they named Rayhoon.
Not knowing the taste of their customers, they decided to serve only two full course meals each night, one with pork and the other with chicken.
They estimated that they would sell a maximum of 60 meals each night. Each chicken dinner requires 15 minutes to prepare, and each pork dinner takes twice as long. There is a total of 20 hours of kitchen staff labor available each day. They thought that they would sell at least 3 chicken dinners for every two pork dinners. They also believe that at least 10 percent of their customers will order pork dinners. The profit from each chicken dinner will be \$12, and the profit from a pork dinner will be \$16.
Formulate a linear programming model for B & B, that will help them estimate the number of meals they should prepare each night and solve this model by computer.
A. They 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. They are concerned about the reliability 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 chicken dinner. Brayden has suggested a price increase that will increase profit for the chicken dinner to \$14. Would this be acceptable, and how much additional profit would be realized?

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