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# ISDS 361 B 35266-lair & Rosen, Inc. (B&R) is a brokerage firm that

Subject: Mathematics / Statistics
Question
lair & 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)Formulate a linear programming model to find the best investment strategy for this client. Let I= Internet fund investment in thousands B= Blue Chip fund investment in thousands If required, round your answers to two decimal places.

(b)Build a spreadsheet model and solve the problem using Solver. What is the recommended investment portfolio for this client? Internet Fund=\$ Blue Chip Fund=\$ What is the annual return for the portfolio?

(c)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?Internet Fund=\$ Blue Chip Fund=\$ Annual Return=\$

(d)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.Internet Fund=\$ Blue Chip Fund=\$ Annual Return=\$

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