Suppose we want to solve the following lpp:
Min $C^T x$ subject to $Ax=b$ where $A$ is a $m \times n$ matrix, $C$ is in $R^n$ and $b$ in $R^m$. Show that if there exists $x$ in $R^n$ with $Ax=b$ and the minimum value is finite (i.e. there is a lower bound) then $C^Tx=k$ ($k$ is a constant) for all solutions $Ax=b$.
How should I proceed? Any help will be appreciated.
Try proving the contrapositive: if the problem is feasible but the objective value is not constant, then the problem is unbounded.