Blair & 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 $70,000 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 10%, whereas the Blue Chip fund has a projected annual return of 8%. The investment advisor requires that at most $45,000 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 340.

(a)Formulate a linear programming model to find the best investment strategy for this client. (Assume N is the amount invested in the internet fund project and B is the amount invested in the Blue Chip fund. Express the amounts invested in thousands of dollars.)

Max ________________ (Please solve.)

s.t.

Available investment funds (Please solve.)

Maximum investment in the internet fund (Please solve.)

Maximum risk for a moderate investor

3406N+4B (Correct answer)

N, B 0

(b)Build a spreadsheet model and solve the problem using Excel Solver. What is the recommended investment portfolio (in dollars) for this client?

internet fund $ _30,000______________ (Correct answer.)

blue chip fund $ 40,000 (Correct answer.)

What is the annual return (in dollars) for the portfolio?$ 6,200 (Correct answer.)

(b) Suppose that a second client with $70,000 to invest has been classified as an aggressive investor. B&R recommends that the maximum portfolio risk rating for an aggressive investor is 370. What is the recommended investment portfolio (in dollars) for this aggressive investor?

internet fund $ ________________ (Please solve.)

blue chip fund $ ________________ (Please solve.)

(d) Suppose that a third client with $70,000 to invest has been classified as a conservative investor. B&R recommends that the maximum portfolio risk rating for a conservative investor is 260. Develop the recommended investment portfolio (in dollars) for the conservative investor.

internet fund $ ________________ (Please solve.)

blue chip fund $ ________________ (Please solve.)