Example
The red constraints are binding, so substitute for $\pi_1$ and $\pi_2$.
\begin{align*}
w_1-w_2&\geq 1\\
w_1-w_2&\leq 6\\
w_1,w_2&\geq 0
\end{align*}
The red constraints are binding, so substitute for $\pi_1$ and $\pi_2$.