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?