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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 $55,000 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%, and the Blue Chip fund has a projected annual return of 9%. The investment advisor requires that at most $25,000 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 5 per thousand dollars invested. The Blue Chip fund has a risk rating of 5 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 5(10) + 5(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 250. (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. If an amount is zero, enter "0". If the constant is "1" it must be entered in the box. Max s.t. .12 I + 1 I+ 1 I + .005 I + I, B .09 B 1 BS OBS .004 B S 2 ✓ $ $ 55000 Available investment funds 25000 Maximum investment in the internet fund Maximum risk for a moderate investor 250 0

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 $55,000 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%, and the Blue Chip fund has a projected annual return of 9%. The investment advisor requires that at most $25,000 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 5 per thousand dollars invested. The Blue Chip fund has a risk rating of 5 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 5(10) + 5(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 250. (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. If an amount is zero, enter "0". If the constant is "1" it must be entered in the box. Max s.t. .12 I + 1 I+ 1 I + .005 I + I, B .09 B 1 BS OBS .004 B S 2 ✓ $ $ 55000 Available investment funds 25000 Maximum investment in the internet fund Maximum risk for a moderate investor 250 0

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter9: Decision Making Under Uncertainty
Section: Chapter Questions
Problem 34P
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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 $55,000 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%, and the Blue Chip fund has a projected annual return of 9%. The investment advisor requires that at most $25,000 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 5 per thousand dollars invested. The Blue Chip fund has a risk rating of 5 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 5(10) + 5(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 250. (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. If an amount is zero, enter "0". If the constant is "1" it must be entered in the box. Max s.t. .12 I + 1 I + 1 I + .005 I + I, B .09 B 1 B 0 B .004 B VI VI VI IV V 55000 Available investment funds 25000 Maximum investment in the internet fund 250 0 Maximum sk for a moderate investor
Transcribed Image Text: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 $55,000 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%, and the Blue Chip fund has a projected annual return of 9%. The investment advisor requires that at most $25,000 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 5 per thousand dollars invested. The Blue Chip fund has a risk rating of 5 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 5(10) + 5(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 250. (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. If an amount is zero, enter "0". If the constant is "1" it must be entered in the box. Max s.t. .12 I + 1 I + 1 I + .005 I + I, B .09 B 1 B 0 B .004 B VI VI VI IV V 55000 Available investment funds 25000 Maximum investment in the internet fund 250 0 Maximum sk for a moderate investor
(d) Suppose that a third client with $55,000 to invest has been classified as a conservative investor. B&R recommends that the maximum portfolio risk rating for a conservative investor is 150. Develop the recommended investment portfolio for the conservative investor. If an amount is zero, enter "0". Internet Fund = $ Blue Chip Fund = $ Annual Return = $ 25000
Transcribed Image Text:(d) Suppose that a third client with $55,000 to invest has been classified as a conservative investor. B&R recommends that the maximum portfolio risk rating for a conservative investor is 150. Develop the recommended investment portfolio for the conservative investor. If an amount is zero, enter "0". Internet Fund = $ Blue Chip Fund = $ Annual Return = $ 25000
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