\( \newcommand{\lra}{\leftrightarrow} \newcommand{\ll}{\mathcal L} \newcommand{\ff}{\mathcal F} \definecolor{cornellred}{RGB}{179,27,27} \newcommand{\cred}[1]{\textcolor{cornellred}{#1}} \newcommand{\tcred}[1]{\textcolor{cornellred}{\textrm{#1}}} \)
Consider the surplus matrix
| $\hspace{-6pt}\cred\ff$ | |||
| $\cred 1$ | $\cred 2$ | ||
| $\cred\ll$ | $\cred 1$ | $10$ | $9$ |
| $\cred 2$ | $9$ | $3$ | |
The optimal match is $\tiny 1\lra 2, 2\lra 1$ with a surplus of 18. The dual constraints are \begin{align*} \scriptscriptstyle w_{\tiny 1}+\pi_{\tiny 1}&\scriptscriptstyle\geq 10&\cred{\scriptscriptstyle w_{\tiny 1}+\pi_{\tiny 2}}&\cred{\scriptscriptstyle \geq 9}\\ \cred{\scriptscriptstyle w_{\tiny 2}+\pi_{\tiny 1}}&\cred{\scriptscriptstyle \geq 9}&\scriptscriptstyle w_{\tiny 2}+\pi_{\tiny 2}&\scriptscriptstyle \geq 3 \end{align*} and the binding constraints are in red.