How to align equations

Question

I am trying to write a set of equations similar to some found in a book I am reading. Below is how the book has formatted the equations:

and here is what I have so far:

How can I align my equations so that "maximize" and "subject to" are aligned, while also aligning the sums? I do not want to display "(KP)" or any equation numbers on the side.

Here is the code I wrote:

\begin{equation*}
\begin{aligned}
    \text{maximize} \sum_{j=1}^{n}p_j x_j \\
    \text{subject to} \sum_{j=1}^{n}w_j x_j \leq c, \\
    x_j \in \{0,1\}, j = 1, \ldots, n.
\end{aligned}
\end{equation*}

Answer 1

Use the align environments from amsmath:

\documentclass{article}
\usepackage{amsmath}

\begin{document}
\begin{align}
  \text{maximize} &\null \sum_{j=1}^n p_j x_j \\
  \text{subject to} &\null \sum_{j=1}^n w_j x_j \leq c, \\
  &\null x_j \in \{0, 1\}, \quad j=1,\dots,n.
\end{align}
\end{document}

Answer 2

The simple solution

As long as the super- and subscripts of the summation signs are narrower than the sign itself, the solution is quite simple:

\documentclass{article}
\usepackage{amsmath}

\begin{document}
\begin{align}
\text{maximize } &\sum_{j=1}^{n}p_j x_j \\
    \text{subject to } &\sum_{j=1}^{n}w_j x_j \leq c, \\
    &x_j \in \{0,1\}, j = 1, \ldots, n.
\end{align}
\end{document}

The more sophisticated solution

As soon as one of the super- or subscripts gets wider than the sign, this will break the alignment (note eq. (2)):

\begin{align}
\text{maximize } &\sum_{j=1}^{n}p_j x_j \\
    \text{subject to } &\sum_{j=10000}^{n}w_j x_j \leq c, \\
    &x_j \in \{0,1\}, j = 1, \ldots, n.
\end{align}

As everything is aligned at the most left part after the & sign, the alignment happens in eq. (2) at the "j" subscript, making the sum signs no longer stand right below each other:

But there is help! The mathtools package provides a command called \mathclap that in principle sets the box width of its argument to zero (for exact explanation cf. http://math.arizona.edu/~aprl/publications/mathclap/perlis_mathclap_24Jun2003.pdf). If we use this, the alignment will work even if the descriptors of the sum sign are wider than the sign itself, by allowing the descriptors to slide over the alignment barrier:

\documentclass{article}
\usepackage{amsmath}
\usepackage{mathtools}

\begin{document}
\begin{align}
\text{maximize } &\sum_{j=1}^{n}p_j x_j \\
    \text{subject to } &\sum_{\mathclap{j=10000}}^{n}w_j x_j \leq c, \\
    &x_j \in \{0,1\}, j = 1, \ldots, n.
\end{align}
\end{document}

Answer 3

You can use

\documentclass{article}
\usepackage{amsmath}

\begin{document}
\begin{alignat}{2}
  text & equation\\
  text & equation\\
       & equatin
\end{alignat}
\end{document}

Additionally, with alignat, you can specify multiple alignment points. If we had 3, we could align equations like this:

f(x) & = & x^2 +2x + 1\\
     & = & (x + 1)^2

Or you could go with even more alignment options depending on your needs.