` \begin{equation} \begin{aligned} v_D(\ll\cup\ff)&=\max_{\pi,w}\sum_{l,f\in\ll\cup\ff}w_l+\pi_f\\[6pt] \text{s.t.}\qquad&\begin{aligned}[t] w_l+\pi_f&\geq v_{lf}\text{ for all $l\in\ll$, $f\in\ff$}\\[6pt] w_l,\pi_f&\geq 0\text{ for all $l\in\ll,f\in\ff$.} \end{aligned} \end{aligned} \end{equation}