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Math Help - Linear Programing Problem, Simplex but with a negative constraint?

  1. #1
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    [SOLVED] Linear Programing Problem, Simplex but with a negative constraint?

    Hi, I have the following question and I need to know if i have augmented it correctly and what my next steps should be.

    Maximise
    Z = x_{1} + 4x_{2}
    subject to
    -3x_{1} + x_{2} \leq 6
    x_{1} + 2x_{2} \leq 4
    and  x_{2} \geq -3

    My steps to solve were

    let x'_{2} = x_{2} + 3

    so then we have:
    Z = x_{1} + 4x'_{2} -12
    -3x_{1} + x'_{2} \leq 9
    x_{1} + 2x'_{2} \leq 10
    and  x'_{2} \geq 0

    i thought this was the correct augmented form of the LPP, however, none of the multiple choice answers i can choose from show this, hence i know it is wrong, but I'm not sure what i have done wrong, all the answers have added more variables.
    Last edited by Stylis10; March 6th 2012 at 06:35 AM.
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  2. #2
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    Re: Linear Programing Problem, Simplex but with a negative constraint?

    I have come up with this as my augmented problem:

    Z = x^+_{1} -  x^-_{1} + 4x'_{2} -12
    -3x^+_{1} + 3x^-_{1} + x'_{2} + x_{3} = 9
    x^+_{1} -  x^-_{1} + 2x'_{2} + x_{4} = 10
    x^+_{1} \geq 0, x^-_{1} \geq 0, x'_{2} \geq 0, x_{3} \geq 0, x_{4} \geq 0

    However, when i try to solve this in a tableau i don't get any of the answers given.
    Am i first supposed to change the first equation so that x^+_{1}, x^-_{1} and x'_{2} coefficients are to equal zero or just some of the variables.
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  3. #3
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    Re: Linear Programing Problem, Simplex but with a negative constraint?

    Solved
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