My Math Forum LP with Big-M Method

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 May 23rd, 2012, 12:28 AM #1 Member   Joined: Jan 2010 Posts: 44 Thanks: 0 LP with Big-M Method Hello! Have some difficulties to obtain some properties of optimal solution for one LP with respect to the other. So - I have a LP: min$cx$ s.t. $Ax=b$, $x\geq 0$ I apply the Big M method to get initial basic feasible solution, so I get a LP': min$cx+M\sum_{i=1}^m{y_i}$, where M is large number s.t. $Ax+y=b$, $x,y\geq 0$ 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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