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.

**Week 8 Assignment**

Blair and Rosen, Inc. (B&R) is a brokerage firm that specializes in investment portfolios designed to meet the specific risk tolerances of its clients. A client who contacted B&R this past week has a maximum of $50,000 to invest. B&R's investment advisor decides to recommend a portfolio consisting of two investment funds: an Internet fund and a Blue Chip fund. The Internet fund has a projected annual return of 12%, while the Blue Chip fund has a projected annual return of 9%. The investment advisor requires that at most $35,000 of the client's funds should be invested in the Internet fund. B&R services include a risk rating for each investment alternative. The Internet fund, which is the more risky of the two investment alternatives, has a risk rating of 6 per thousand dollars invested. The Blue Chip fund has a risk rating of 4 per thousand dollars invested. For example, if $10,000 is invested in each of the two investment funds, B&R's risk rating for the portfolio would be 6(10) + 4(10) = 100. Finally, B&R developed a questionnaire to measure each client's risk tolerance. Based on the responses, each client is classified as a conservative, moderate, or aggressive investor. Suppose that the questionnaire results classified the current client as a moderate investor. B&R recommends that a client who is a moderate investor limit his or her portfolio to a maximum risk rating of 240.

a. What is the recommended investment portfolio for this client? What is the annual return for the portfolio?

b. Suppose that a second client with $50,000 to invest has been classified as an aggressive investor. B&R recommends that the maximum portfolio risk rating for an aggressive investor is 320. What is the recommended investment portfolio for this aggressive investor? Discuss what happens to the portfolio under the aggressive investor strategy.

c. Suppose that a third client with $50,000 to invest has been classified as a conservative investor. B&R recommends that the maximum portfolio risk rating for a conservative investor is 160. Develop the recommended investment portfolio for the conservative investor. Discuss the interpretation of the slack variable for the total investment fund constraint.

**Week 8 Assignment - Writeup**

You will be turning in two (2) deliverables, a short writeup of the project and the spreadsheet showing your work.

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.

Subject | Mathematics |

Due By (Pacific Time) | 03/05/2015 03:00 pm |

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