Can anyone give me a suggestion?
Let \begin{equation} \min \hspace{0.3cm} \{c^Tx: \text{ s.t. } Ax = b, x \geq 0 \} \end{equation} Suppose that $x$ is a feasible solution to the previous LP, with $A$ an $m \times n$ matrix of rank $m$. Show that there is a feasible solution $y$ having the same value (i.e. $c^Ty = c^Tx$) and having at most $m+1$ positive components.
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