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\begin{alignat*}{3}
 & \text{minimize} & ∑_{j=1}^{m} w_{j}x_{j}& \\
 & \text{subject to} \quad& ∑_{\mathclap{{j:e_{i} ∈ S_{j}}}}x_{j}& \geq 1, & i &=1 ,..., n\\
                 && x_{j}& ∈ \{0,1\},\quad & j &=1 ,..., m
\end{alignat*}

\begin{alignat*}{2}
  & \text{minimize: } & & ∑_{j=1}^{m} w_{j}x_{j} \\
   & \text{subject to: }& \quad & ∑_{\mathclap{{j:e_{i} ∈ S_{j}}}}\begin{aligned}[t]
                    x_{j} & \geq 1,& i & =1, \dots, n\\[3ex]
                  x_{j} & ∈ \{0,1\}, & \quad j &=1 ,\dots, m
                \end{aligned}
\end{alignat*}

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