Question

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 $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 $10,000 is invested in each of the two investment funds, B&R's risk rating for the portfolio would be 6(10) 4(10) 100. Finally, B&R developed a questionnaire to measure each client's risk tolerance. Based on the responses, each client is classified as a conservative, moderate, or aggressive investor Suppose that the questionnaire results classified the current client as a moderate investor. B&R recommends that a client who is a moderate investor limit his or her portfolio to a maximum risk rating of 240 (a) Formulate a linear programming model to find the best investment strategy for this client. Let 1 = Internet fund investment in thousands B Blue Chip fund investment in thousands If required, round your answers to two decimal places - Select your answer- s.t. Available investment funds B | -Select your answer- B | -Select your answer- B 1 -Select your answer- Maximum investment in the internet fund Maximum risk for a moderate investor I, B - Select your answer 0 (b) Build a spreadsheet model and solve the problem using Solver. What is the recommended investment portfolio for this client? Internet Fund$ 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

Answer 1

(a)and (b)
Decision variables:
I = Money invested in Internet Funds in thousands				I =	35
B = Money invested in Blue Chip Funds in thousands				B =	3.333333
R = Return on investment in thousands				R =	4.5
Objective function:				Actual Funds Invested in thousands	38.33333
Maximize R = 0.12I + 0.09B				Actual Investment in Internet Funds	35
				Risk Rating	240
Constraints:
I + B ≤ 50
I ≤ 35				Optimum solution: I = $35000, B = $3333.33, R = $4500
6I + 10B ≤ 240
I, B ≥ 0
(c)
Decision variables:
I = Money invested in Internet Funds in thousands				I =	35
B = Money invested in Blue Chip Funds in thousands				B =	11
R = Return on investment in thousands				R =	5.19
Objective function:				Actual Funds Invested in thousands	46
Maximize R = 0.12I + 0.09B				Actual Investment in Internet Funds	35
				Risk Rating	320
Constraints:
I + B ≤ 50
I ≤ 35				Optimum solution: I = $35000, B = $11000, R = $5190
6I + 10B ≤320
I, B ≥ 0