Mat 540 week 8 assignment 1

Assignment 1 Linear Programming Case Study The Owner Of Chips

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.

The owner of Chips etc. produces 2 kinds of chips: Lime (L) and Vinegar (V). He has a limited amount of the 3 ingredients used to produce these chips available for his next production run: 4600 ounces of salt, 9400 ounces of flour, and 2200 ounces of herbs. A bag of Lime chips requires 1.5 ounces of salt, 5 ounces of flour, and 2 ounces of herbs to produce; while a bag of Vinegar chips requires 4 ounces of salt, 6 ounces of flour, and 2 ounces of herbs. Profits for a bag of Lime chips are $0.48, and for a bag of Vinegar chips $0.59.

a) What is the formulation for this problem?

b) For the production combination of 800 bags of Lime and 600 bags of Vinegar, which resource is not completely used up and how much is remaining?

c) For the production combination of 800 bags of Lime and 600 bags of Vinegar, which resource is not completely used up and how much is remaining?

d) Discuss: Slack (if any); shadow price, and sensitivity analysis results using the program of your choice.