Align a linear program

Something like this. Use of array

Code

\documentclass[a4paper]{article}
\usepackage[paper size={10cm,5cm}]{geometry}
\pagestyle{empty}
\usepackage{amsmath,amssymb}
\begin{document}
\begin{equation*}
\begin{array}{ll@{}ll}
\text{minimize}  & \displaystyle\sum\limits_{j=1}^{m} w_{j}&x_{j} &\\
\text{subject to}& \displaystyle\sum\limits_{j:e_{i} \in S_{j}}   &x_{j} \geq 1,  &i=1 ,\dots, n\\
                 &                                                &x_{j} \in \{0,1\}, &j=1 ,\dots, m
\end{array}
\end{equation*}
\end{document}

The = signs are not quite vertically aligned. Here is a solution with alignat* that gives a correct alignment, and has a somewhat simpler syntax. I also propose a variant, where the sums are aligned, and the x_j are only partially aligned, that look better in my opinion:

\documentclass[a4paper]{article}
\usepackage[paper size={10cm,5cm}]{geometry}
\pagestyle{empty}
\usepackage{mathtools,amssymb}

\begin{document}

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

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

\end{document} 

Variant:

Using optidef package you can obtain the same result like this:

\documentclass[a4paper,12pt]{article}
\usepackage{amsmath,amssymb}
\usepackage{optidef}


\begin{document}
\begin{mini*}
{}{\sum_{j=1}^{m} w_{j}x_{j}}{}{}
\addConstraint{\sum_{j:\, e_{i} \in S_{j}} } {x_{j}\geq 1,}{}{\mkern53mu i=1 ,\ldots, n}
\addConstraint{ }{x_{j}}{ \in \{0,1\},}{\quad j=1 ,\ldots, m}
\end{mini*}
\end{document}