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Math Help - Linear Programing - Negative Numbers Help

  1. #1
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    Question Linear Programing - Negative Numbers Help

    Hi,

    I have a question about what to do with a constraint that is negative.

    A: -3x1 + x2 = 90

    So I get x1= -30, and x2 = 90.

    I have a feeling this isn't right since linear models should not have negative numbers.

    Can anyone help me out?
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by guthrie23 View Post
    Hi,

    I have a question about what to do with a constraint that is negative.

    A: -3x1 + x2 = 90

    So I get x1= -30, and x2 = 90.

    I have a feeling this isn't right since linear models should not have negative numbers.

    Can anyone help me out?
    Could you post the whole question? If we can see the problem in its entirety, we may be able to assist you more since there are methods that help us deal with LP problems that have "negative" constraits (methods like the Dual-Simplex method).
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  3. #3
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    Constraint A: -3X1 + X2 =< 90
    Constraint B: 4X1 - 2X2 >= 120
    Constraint C: X1 + 2X2 =< 150
    All variables are required to be non-negative. Let the objective function be Min: 2X1 - 3X2. What are the corner points of feasible solution region?
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  4. #4
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    X1 = 54, x2 = 48 : 2x1 - 3x2 = -36
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by guthrie23 View Post
    Constraint A: -3X1 + X2 =< 90
    Constraint B: 4X1 - 2X2 >= 120
    Constraint C: X1 + 2X2 =< 150
    All variables are required to be non-negative. Let the objective function be Min: 2X1 - 3X2. What are the corner points of feasible solution region?
    Rewrite the constraints:

    x_2 <= 90 + 3 x_1

    x_2 <= -60 + 2 x_1

    x_2 <= 75 - x_1/2

    x_1 >=0, x_2>=0

    Plot these constraints and the vertices of the feasible region will be obvious.

    CB
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    Wilmer, How did you get those answers?
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  7. #7
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    Loopy-de-loop program; a bit like:

    Loop X1, X2
    If -3*X1 + X2 > 90
    or 4*X1 - 2*X2 < 120
    or X1 + 2*X2 > 150
    then get out of here, else
    M = 2*X1 - 3*X2
    Store M if lower than last M
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  8. #8
    Grand Panjandrum
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    Quote Originally Posted by guthrie23 View Post
    Wilmer, How did you get those answers?
    You will note that Wilmer's post does not answer the question you posted.

    CB
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