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Math Help - Linear Programming Help

  1. #1
    jj007
    Guest

    Linear Programming Help

    I can't seem to get the model correct for this problem.

    A portion of an inheritance will be used to set up a trust fund for two children. The two fund opportunities are: (1) a bond fund with a projected return of 6%, (2) a stock fund with a projected return of 10%. Whatever is decided what portion will be committed to the trust fund, at least 30% of that amount will be invested in the bond fund. In addition, a mix will be selected that will enable a total return of at least 7.5%.

    a. Formulate a linear programming model to determine the percentage that should be allocated to each of the possible alternatives.
    b. Solve using the graphical solution procedure.
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  2. #2
    MHF Contributor
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    Where are you hung up?

    Write down some definitions. <== Note: This is ALWAYS a great place to start.

    B is the proportion in the Bond Fund
    S is the proportion in the Stock Fund
    B+S = 1, of course.
    B >= 0
    S >= 0

    Write down the requirements and have at it.

    "at least 30% of that amount will be invested in the bond fund"
    B/(B+S) >= 0.30 or B >= (B+S)*0.30

    "a mix will be selected that will enable a total return of at least 7.5%"
    B*0.06 + S*0.10 >= (B+S)*0.075

    After a little algebra, you'll be ready to start drawing pictures. Let's see what you get.
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