Align with long equations / join cells?

Question

I'm having trouble using the align environment to stack up equations for a linear program. The issue I'm having is that the contents of the center column in the top row are so long that they push the lower rows into the margin and affect the alignment of the row numbers. What I'd like to do is maybe put in extra sub-columns in the lower rows and/or join them such that the "for each" statements are aligned, but under the overhang of the top equation. I tried a handful of commands, but no success. Here is the current state of affairs...

By the way... I'm pretty much a noob at LaTex. I only have reason to use it occasionally, and I usually throw code at it till it works, so assume nothing in your answer! :)

\usepackage{amsmath}

\begin{flalign}
max  \quad &Z=\sum_{d \in D} w_1*dep_d - \sum_{V, a \in G^v} w_2*x_{v,a} \sum_{S, a \in G^s} w_3*x_{s, a}\\
s.t. \quad & x_{s,a} \le x_{v,a}                             &\forall s \in S, v \in V, a \in CN\\
           &count_{cfg} * x_{v,a} \le \sum_{s \in S} x_{s,a} &\forall v \in V, a \in CN, cfg \in C_d
\end{flalign}

Answer 1

(Remark: I modified this answer to incorporate a couple of pieces of information provided by the OP, e.g., that a - symbol was missing between of the summation terms in row 1, and that * symbols denote multiplication and aren't strictly needed.)

Here's a solution that employs an align environment and a single & alignment marker per row.

\documentclass{article} % or some other suitable document class
\usepackage{mathtools}  % for \smashoperator macro; loads amsmath automatically
\newcommand\vn[1]{\textit{#1}} % 'variable name'

\begin{document}

\begin{align}
\max\quad &Z= \sum_{d \in D} w_1\,\vn{dep}_d 
             -\smashoperator{\sum_{v,a\in G^v}} w_2\,x_{v,a}
             -\smashoperator{\sum_{s,a\in G^s}} w_3\,x_{s,a}\\
\textup{s.t.}\quad 
          & x_{s,a} \le x_{v,a} 
            \qquad\forall s \in S,\ v \in V,\ a \in \vn{CN}\\
          & \vn{count}^{}_{\vn{cfg}} \, x_{v,a} \le \sum_{s \in S} x_{s,a} 
            \qquad\forall v \in V,\ a \in \vn{CN},\ \vn{cfg} \in C_d
\end{align}
\end{document}

Answer 2

After fumbling w/ multispan and others without success, I stumbled on span which works and allows the long segment to "span" the last column.

This works fine:

    \begin{flalign}
max  \quad &Z=\sum_{d \in D} w_1dep_d - \sum_{V, a \in G^v} w_2x_{v,a} -\sum_{S, a \in G^s} w_3x_{s, a}\span\\
s.t. \quad & x_{s,a} \le x_{v,a}                             &\forall s \in S, v \in V, a \in CN\\
           &count_{cfg} x_{v,a} \le \sum_{s \in S} x_{s,a} &\forall v \in V, a \in CN, cfg \in C_d
\end{flalign}

Answer 3

I think you should use the dedicated package for optimisation problems – optidef:

    \documentclass{article}
    \usepackage{amsmath}
    \usepackage[short]{optidef}

        \begin{document}

    \begin{maxi!}{}
    {Z=\sum_{d \in D} w_1\cdot\operatorname{dep}_d - \sum_{V, a \in G^v} w_2\cdot x_{v,a} \sum_{S, a \in G^s} w_3*x_{s, a}}{}{}
    \addConstraint{x_{s,a}}{ \le x_{v,a}}{\forall s \in S, v \in V, a \in CN}
    \addConstraint{\operatorname{count}_{cfg}\cdot x_{v,a}}{ \le \sum_{s \in S} x_{s,a}\quad}{ \forall v \in V, a \in CN, %
    cfg \in C_d}
    \end{maxi!}

    \end{document}