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17 July, 08:57

George Johnson recently inherited a large sum of money; he wants to use a portion of this money to set up a trust fund for his two children. The trust fund has two investment options: (1) a bond fund and (2) a stock fund. The projected returns over the life of the investments are 6% for the bond fund and 10% for the stock fund. Whatever portion of the inheritance George finally decides to commit to the trust fund, he wants to invest at least 30% of that amount in the bond fund. In addition, he wants to select a mix that will enable him to obtain a total return of at least 7.5%. Formulate a linear programming model that can be used to determine the percentage that should be allocated to each of the possible investment alternatives. If required, round your answers to three decimal places. Value of optimal solution is %

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  1. 17 July, 09:26
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    Return on investment

    X * 0.06 + (1-X) * 0.1 = 0.075

    where:

    1>X >0.30

    X is the percentage invest on bond fund

    It needs to invest 62.5% in the bond fund

    and 37.5% in the stock und to achieve 7.5% return

    Explanation:

    We have a certain amount divided into two option.

    being X the bond fund the rmainder (1 - X) will be invested in the stock fund

    We want at least an X of 30%

    and achieve 7.5% return

    0.06X + 0.1 - 0.1X = 0.075

    0.1-0.075 = 0.04X

    X = 0.025/0.04 =.625 = 62.5%
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