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Thread: Big-M Method

  1. #1
    Junior Member
    Jan 2010

    Big-M Method

    Hello, everyone.
    Again the same problem - what seems to be obvious for everyone, do not seems obvios for me
    So - I have a LP:
    min$\displaystyle cx$
    s.t. $\displaystyle Ax=b$, $\displaystyle x\geq 0$

    I apply the Big M method to get initial basic feasible solution, so I get a LP':
    min$\displaystyle cx+M\sum_{i=1}^m{y_i}$, where M is large number
    s.t. $\displaystyle Ax+y=b$, $\displaystyle x,y\geq 0$
    Simplex algorithm is applied.
    1)In all text-books it is said, that one can easily see, that if LP' has an optimal solution with y\neq 0, then LP is unfeasible. Why is that?
    2)If it is known that LP' is not bounded, then it follows LP is unbounded or unfeasible. What is justification for that?

    Maybe someone can explain or give a hint?
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  2. #2
    Junior Member
    Jan 2010

    Re: Big-M Method

    ok, I think I managed this by myself. One should simply assume the opposite in both cases and then it really comes quite obvious.
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