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Math Help - two-phase method

  1. #1
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    two-phase method

    Use the two-phase method to find an optimal solution to the linear programming problem

    minimize z = 3x1 + 2x2
    subject to
    x1 + 3x2 + 2x3 >= 7
    2x1 + x2 + x3 >= 4
    x1 >= 0 , x2 >= 0, x3 >= 0

    Thanks very much
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  2. #2
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    minimize z = 3x1 + 2x2
    subject to
    x1 + 3x2 + 2x3 >= 7
    2x1 + x2 + x3 >= 4
    x1 >= 0 , x2 >= 0, x3 >= 0

    letting x1 be x, x2 as y, and x3 as w
    it would look like
    x + 3y + 2w > 7
    2x + y + w > 4
    z = 3x + 2y right?

    perhaps u can set up a matrix
    but i'm not sure if its possible for the greater than signs
    and for the third row, the use of both equations would
    result in 2y + 3w > 10
    as
    [1 3 2 7]
    [2 1 1 4]
    [0 2 3 10]

    it would solve for each x y and w
    x = 1/3, y = 0 and w= 10/3
    but i'm not sure how you would in put it into ur answer
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