# Math Help - Big-M Method

1. ## 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 $cx$
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?

2. ## 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.