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Math Help - How to set up a linear programming model

  1. #1
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    How to set up a linear programming model

    For this problem, all I need to do is to set up the model. I don't have to solve it or put it in standard or canonical form or anything like that, just simply set it up in the model. I just can't seem to figure this one out.

    The administrator of a $200,000 trust fund set up by Mr. Smith's will must adhere to certain guidelines. The total amount of $200,000 need not be fully invested at any one time. The money may be invested in three different types of securities: a utilities stock paying a 9% dividend, an electronics stock paying 4% dividend, and a bond paying 5% interest. Suppose that the amount invested in the stocks cannot be more than half the total amount invested; the amount invested in the utilities stock cannot exceed $40,000; and the amount invested in the bond must be at least $70,000. What investment policy should be pursued to maximize the return?

    I need to set it up in the form :Maximize
    subject to
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Denote:

    x_1 : money invested in utilities stock
    x_2 : money invested in electronics stock
    x_3 : money invested in a bond

    The problen is maximize z=0.9x_1+0.4x_2+0.5x_3 with the restrictions:

    x_1+x_2+x_3\leq 200,000

    x_1+x_2\leq (1/2)(x_1+x_2+x_3)

    x_1+x_1\leq 40,000

    x_1\geq 0,x_2\geq 0,x_3 \geq70,000


    Fernando Revilla
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  3. #3
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    Quote Originally Posted by FernandoRevilla View Post
    Denote:

    x_1 : money invested in utilities stock
    x_2 : money invested in electronics stock
    x_3 : money invested in a bond

    The problen is maximize z=0.9x_1+0.4x_2+0.5x_3 with the restrictions:

    x_1+x_2+x_3\leq 200,000

    x_1+x_2\leq (1/2)(x_1+x_2+x_3)

    x_1+x_1\leq 40,000

    x_1\geq 0,x_2\geq 0,x_3 \geq70,000


    Fernando Revilla
    Thanks so much, I couldn't wrap my head around that one. But two quick questions..(1) I would say this is in standard form because we don't know what x1 x2 x3 are in the second constraint on the right side. But (2) why is the last constraint x1+x1? Thanks again!
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by tn11631 View Post
    (1) I would say this is in standard form because we don't know what x1 x2 x3 are in the second constraint on the right side

    That depends on the way you define standard form.


    But (2) why is the last constraint x1+x1? Thanks again!

    A typo, it should be x_1\leq 40,000


    Fernando Revilla
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