A matching is optimal if it maximizes total surplus.
\begin{equation}\label{eq:1} \begin{aligned} v(\ll\cup\ff)&=\max_x\sum_{l,f}v_{lf}x_{lf}\\ \text{s.t.}\qquad&\begin{aligned}[c] \sum_fx_{lf}&\leq 1\text{ for all $l\in\ll$,}\\ \sum_lx_{lf}&\leq 1\text{ for all $f\in\ff$,}\\ x_{lf}&\in\{0,1\}\text{ for all $l\in\ll,f\in\ff$.} \end{aligned} \end{aligned} \end{equation}A matching $x$ is optimal iff it solves this optimization problem.