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Math Help - Financial Linear Programming assignment-need help here....

  1. #1
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    Financial Linear Programming assignment-need help here....

    A company invests in short-term trade credits (TC), corporate bonds (CB), gold stocks (GS) and construction loans (CL). To encourage a diversified portfolio, the board of directors has placed limits on the amount that can be committed to any one type of investment. The company has $5,000,000 available for immediate investment and wishes to do two things:
    1. Maximise the interest earned on the investments made over the next six months, and
    2. Satisfy the diversification requirements as set out by the board of directors.

    The specifics of the investment possibilities are:-

    Investment Interest Earned (%)
    Trade Credit (TC) 7
    Corporate Bonds (CB) 11
    Gold Stocks (GS) 19
    Construction Loans (CL) 15

    Investment Maximum Investment ($ Millions)
    Trade Credit (TC) 1.0
    Corporate Bonds (CB) 2.5
    Gold Stocks (GS) 1.5
    Construction Loans (CL) 1.8


    In addition the board specifies that at least 55% of the funds invested must be in gold stocks and construction loans, and that no less than 15% be invested in trade credit.

    I came out with the following....


    Decision Variables

    X1= Amount of dollars in millions invested in Trade Credit
    X2= Amount of dollars in millions invested in Corporate Bonds
    X3= Amount of dollars in millions invested in Gold Stocks
    X4= Amount of dollars in millions invested in Construction Loans

    Objective Function

    0.07(X1) + 0.11(X2) + 0.19(X3) + 0.15(X4) = Z (maximize interest earned on investment)

    Constraints

    X1, X2, X3, X4 > 0 (Non-negativity constraint)
    X1 + X2 + X3 + X4 < 5 (Investment Budget constraint)
    X1 < 1 (Maximum investment constraint)
    X2 < 2.5 (Maximum investment constraint)
    X3 < 1.5 (Maximum investment constraint)
    X4 < 1.8 (Maximum investment constraint)
    -0.55X1-0.55X2+0.45X3+0.45X4
    0.85X1-0.15X2-0.15X3-0.15X4

    I am required to solve this using excel solver....And that's what i got below....

    Decision Variables
    x1 0.75
    x2 0.95
    x3 1.5
    x4 1.8
    objective fuction
    0.07 0.11 0.19 0.15
    max investement
    0.712

    Constraints
    LHS RHS
    5.00 1 1 1 1 5
    0.75 1 0 0 0 1
    0.95 0 1 0 0 2.5
    1.50 0 0 1 0 1.5
    1.80 0 0 0 1 1.8
    0.55 -0.55 -0.55 0.45 0.45 0
    0.00 0.85 -0.15 -0.15 -0.15 0

    Now i am not sure whether the LHS(highlight portion) of the excel should match the data in X3 + X4, should it be 3.3 instead of the 0.55 but the formula i entered is according to the constraints i developed which is -0.55X1-0.55X2+0.45X3+0.45X4 and for the last row should the highlight portion be 0.75, as the formula on the Left hand side is
    0.85X1-0.15X2-0.15X3-0.15X4

    Can pls tell me whether my constraint is correct in this sense? Is the whole ans correct? Pls help...tks...
    Last edited by nonolee; August 5th 2008 at 09:22 PM. Reason: error
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  2. #2
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    Now i am not sure whether the LHS(highlight portion) of the excel should match the data in X3 + X4
    The constraints you have used for the 55% and 15% are unusual but not wrong. The normal method of programming them in would have changed the highlighted data to what you describe at the bottom.

    Good luck with the rest of the assignment
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  3. #3
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    So..in this sense...

    -0.55(X1) 0.55(X2) + 0.45(X3) + 0.45(X4) > 0
    (Gold stocks and construction loans constraint)

    0.85(X1)0.15(X2)0.15(X3)-0.15(X4) > 0
    ( Trade credit constraint)

    So for the last two constraints is correct? or is there another to express the constraints?
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  4. #4
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    The constraints as you have them are correct. There is another way to describe them that is far more common, but I would rather not explain this right now because this is your assignment. I think it is much better for you to use the expression you came up with yourself. If you still want to know after you have handed it in, feel free to ask me.
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  5. #5
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    i know the other way is take 55% of the total investment value you have
    that's like

    X3 + X4>= 2750000 since the total avaliable amt is 5 million but that's being used when the investment is to use up the whole amt..but in this case it is not...can pls explain?
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  6. #6
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    That was the other way I was thinking of and if you code in that value for the restraint then the highlighted part will match X3+X4.

    It is fairly easy to see that the correct answer will have all of the money invested without doing any excel stuff at all but you're right, it does make more sense to use your method if you want to have everything done electronically so that it can be scaled up to bigger problems more easily.
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  7. #7
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    so in another i might be right for my constraint?? but why i do not the amt on the Left hand side...??
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  8. #8
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    so in another i might be right for my constraint?? but why i do not the amt on the Left hand side...??
    I'm not at all sure what you are saying here. I think you are asking about what the amount on the left hand side is.

    The amount on the left hand side is the value of the expression you are constraining in the constraint.

    Constraints
    LHS RHS
    5.00 1 1 1 1 5 <------------- 1
    0.75 1 0 0 0 1
    0.95 0 1 0 0 2.5
    1.50 0 0 1 0 1.5
    1.80 0 0 0 1 1.8
    0.55 -0.55 -0.55 0.45 0.45 0 <-------------2
    0.00 0.85 -0.15 -0.15 -0.15 0
    so in the line marked 1 above, the LHS is 5.00 because 1*x1+1*x2+1*x3+1*x4=5

    In the line marked 2, the LHS is 0.55 because -0.55*x1+-0.55*x2+0.45*x3+0.45*x4 = 0.55
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  9. #9
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    ya...that's wat i been wondering if let's said my constraints are correct...shl it i be getting on the LHS amt to be 55% of the total amt (5million) which is 2.75 Million...
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