\( \newcommand{\lra}{\leftrightarrow} \newcommand{\ll}{\mathcal L} \newcommand{\ff}{\mathcal F} \definecolor{cornellred}{RGB}{179,27,27} \newcommand{\cred}[1]{\textcolor{cornellred}{#1}} \newcommand{\tcred}[1]{\textcolor{cornellred}{\textrm{#1}}} \)

Example 1

Here is an example with three firms and four workers.

$\cred\ff$
$\cred x$ $\cred y$ $\cred z$
$\cred a$ $1$ $8$ $3$
$\cred\ll$ $\cred b$ $3$ $1$ $8$
$\cred c$ $8$ $3$ $1$
$\cred d$ $7$ $7$ $7$

The optimal match is $\tiny a\lra y,\quad b\lra z,\quad c\lra x$.