Week 8 Assignment 1

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.

Complete the “Julia’s Food Booth” case problem on page 109 of the text. Answer ONLY the following three questions:

(A) Formulate and solve a linear programming model for this case problem. Solve the problem using Excel.

(B) Write the sensitivity ranges for the objective function coefficients and the constraint quantity values.

(C) If Julia were to borrow some 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 constraints her from borrowing even more money than this amount (indicated in your answer to the previous question)?

You are required to set up your problem in Excel and find the solution using Solver. Clearly label the cells in your Excel spreadsheet. You will turn in the entire spreadsheet showing the setup of the model, and the results. Please read the grading rubric in your course guide and make sure that you have correctly completed all what is required in the rubric.

You will be turning in two deliverables, a short write-up of the project and the Excel spreadsheet showing your work.