Assignment - Linear Programming Case Study

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 write up of the project and the spreadsheet showing your work.

Write up.

Your write-up 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

A candy manufacturer has 200 pounds of chocolate-covered cherries and 180 pounds of chocolate-covered mints in stock. He decides to sell them in the form of two different mixtures. One mixture will contain half cherries and half mints by weight and will sell for $1.80 per pound. The other mixture will contain one-third cherries and two-thirds mints by weight and will sell for $1.45 per pound. How many pounds of each mixture should the candy manufacturer prepare in order to maximize his sales revenue?

a. Is this a maximization or minimization model?

b. What are the constraints for this model?

c. Show the relevant functions as you did in HW6

d. What are your main test points and why did you select these points?

e. What is the optimization formula?

f. What is the shadow price?

g. Provide a graphical model.

h. Change the price for chocolate to $2.10 and run the model once again. Explain how changing the price affects the output? 

i. Run a sensitivity report on the original model.

j. Provide a written explanation of the steps taken to discover the optimal result.