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Math Help - HELP!please Linear Programming

  1. #1
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    HELP!please Linear Programming

    Hey, I'm new to this forum, I'm having some trouble with this problem. I'm not very good at math and I dont really get this problem. Thanks for any help anyone can offer.


    Blair & Rosen, Inc. (B&R), is a brokerage firm that specializes in investment portfolios de-signed to meet the specific risk tolerances of its clients. A client who contacted B&Rthispast week has a maximum of $50,000 to invest. B&Rís investment advisor has decided torecommend a portfolio consisting of two investment funds: an Internet fund and a BlueChip fund. The Internet fund has a projected annual return of 12%, while the Blue Chipfund has a projected annual return of 9%. The investment advisor requires that at most$35,000 of the clientís funds should be invested in the Internet fund. B&Rservices includea risk rating for each investment alternative. The Internet fund, which is the more risky ofthe two investment alternatives, has a risk rating of 6 per thousand dollars invested. TheBlue Chip fund has a risk rating of 4 per thousand dollars invested. For example, if $10,000is invested in each of the two investment funds, B&Rís risk rating for the portfolio wouldbe 6(10)4(10)100. Finally, B&Rhas developed a questionnaire to measure eachclientís risk tolerance. Based on the responses, each client is classified as a conservative,moderate, or aggressive investor. Suppose that the questionnaire results have classified thecurrent client as a moderate investor. B&Rrecommends that a client who is a moderate in-vestor 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 re-turn for the portfolio?


    b. Suppose that a second client with $50,000 to invest has been classified as an aggres-sive investor. B&Rrecommends that the maximum portfolio risk rating for an aggres-sive investor is 320. What is the recommended investment portfolio for this aggressiveinvestor? 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 conservativeinvestor. B&Rrecommends that the maximum portfolio risk rating for a conservative in-vestor is 160. Develop the recommended investment portfolio for the conservative investor.Discuss the interpretation of the slack variable for the total investment fund constraint
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by livingtwo View Post
    Hey, I'm new to this forum, I'm having some trouble with this problem. I'm not very good at math and I dont really get this problem. Thanks for any help anyone can offer.


    Blair & Rosen, Inc. (B&R), is a brokerage firm that specializes in investment portfolios de-signed to meet the specific risk tolerances of its clients. A client who contacted B&Rthispast week has a maximum of $50,000 to invest. B&Rís investment advisor has decided torecommend a portfolio consisting of two investment funds: an Internet fund and a BlueChip fund. The Internet fund has a projected annual return of 12%, while the Blue Chipfund has a projected annual return of 9%. The investment advisor requires that at most$35,000 of the clientís funds should be invested in the Internet fund. B&Rservices includea risk rating for each investment alternative. The Internet fund, which is the more risky ofthe two investment alternatives, has a risk rating of 6 per thousand dollars invested. TheBlue Chip fund has a risk rating of 4 per thousand dollars invested. For example, if $10,000is invested in each of the two investment funds, B&Rís risk rating for the portfolio wouldbe 6(10)4(10)100. Finally, B&Rhas developed a questionnaire to measure eachclientís risk tolerance. Based on the responses, each client is classified as a conservative,moderate, or aggressive investor. Suppose that the questionnaire results have classified thecurrent client as a moderate investor. B&Rrecommends that a client who is a moderate in-vestor 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 re-turn for the portfolio?
    Let I be the amount invested in the Internet fund and B that invested in the
    Blue chip fund in dollars.

    Now go through this translating each statement into a constraint or
    an objective to be maximised or minimised.

    To get you started, as there is at most $50000 to be invested you have:

    I >= 0
    B >= 0
    I + B <= 50000


    now carry on from there.

    RonL
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