Aligning linear program with numbers

Question

How can I fit my linear program to my sheet but still have numbers aligned on the right?

\documentclass{article}

% page layout
\usepackage[paper=a4paper,left=50mm,right=20mm,top=20mm,bottom=10mm]{geometry}

% fancy math
\usepackage{amsfonts}
\usepackage{amsmath}
\usepackage{amssymb}

\begin{document}

\begin{alignat}{2}
&\textbf{Minimize} \\
&z =\sum\limits_{i \in I}\sum\limits_{t \in W_i^{work}} c^{period} * x_{i,t}^{work} + \sum\limits_{i \in I} c^{over} * o_i + \sum\limits_{i \in I} c^{staff} * v_i^{staff} + \sum\limits_{d \in D} c^{device} * v_d^{device} \\
&\textbf{subject to}  \\
&\sum\limits_{i \in I_{q':q'=q}} (( \sum\limits{r=t}^{t+W_z^{demand}} x_{i,r}^{work} - y_{i,t}^{break} ) * v_i^{staff}) \geq b_{q,t,z}^{staff} && \forall q \in Q,t \in T, z \in Z \\
&H^{break} * \sum\limits{t \in W_i^{shift}} y_{i,t}^{shift} = \sum\limits{t \in W_i^{break}} y_{i,t}^{break} && \forall i \in I \\
&D_i^{min} \leq \sum\limits{t \in T} y_{i,t}^{shift} \leq D_i^{max} && \forall i \in I
\end{alignat}

\end{document}

That's what I have so far:

Maybe splitting some formulas is a solution? How tiny can I make the font till it is no longer readable?

I followed this question using alignat, sadly there is no numbering and it is much smaller.

Edit #1:
\quad helped a lot, but one line is missing.

Answer 1

I would do the following

• Replace the three instances of && before \forall with \quad. Optionally, since there's now only one alignment point left, replace {alignat}{2} with align.

• Add \notag instructions to the two lines that contain just text ("minimize", "subject to")

• Force all words in superscript position to be typeset in text-upright instead of math-italic mode. I would do this even if it didn't help make the first equation fit within the text block (which it does, happily). If you strongly prefer text-italics over text-upright mode for the words in the superscript positions, replace \textnormal in the definition of the \tn macro with \textit.

• Enlarge the parentheses in the first condition line using \Bigl and \Bigr. To snug up the first and second summation symbols in that line, insert \!\!\! -- three negative thinspaces.

• To force the limits of summation of the two summation expressions in the first math row to be set at the same depth, replace {i \in I} with {i \in I^{\mathstrut}}. A \mathstrut is an invisible object with the height and depth of a parenthesis (().

• Finally, I would delete all \limits directives, as they are redundant and just provide clutter. The material in align and alignat environments is typeset in \displaystyle by default, meaning that all summation signs will be set in "large" form and all limits of summation will be set below (and, if present, above) the summation symbols rather than side-set on the right.

\documentclass{article}
\usepackage[paper=a4paper,left=50mm,right=20mm,
            top=20mm,bottom=10mm]{geometry}
\newcommand\tn[1]{\textnormal{#1}} % shortcut macro
\usepackage{amsmath}}
\begin{document}

\begin{align}
&\textbf{Minimize} \notag \\
&z =\sum_{i \in I^{\mathstrut}}\sum_{t \in W_i^{\tn{work}}} c^{\tn{period}} * x_{i,t}^{\tn{work}} + \sum_{i \in I} c^{\tn{over}} * o_i + \sum_{i \in I} c^{\tn{staff}} * v_i^{\tn{staff}} + \sum_{d \in D} c^{\tn{device}} * v_d^{\tn{device}} \\
&\textbf{subject to} \notag \\
&\sum_{i \in I_{q':q'=q}} \!\!\! \Bigl(\Bigl( \sum{r=t}^{t+W_z^{\tn{demand}}} x_{i,r}^{\tn{work}} - y_{i,t}^{\tn{break}} \Bigr) * v_i^{\tn{staff}}\Bigr) \geq b_{q,t,z}^{\tn{staff}} \quad \forall q \in Q,t \in T, z \in Z \\
&H^{\tn{break}} * \sum{t \in W_i^{\tn{shift}}} y_{i,t}^{\tn{shift}} = \sum{t \in W_i^{\tn{break}}} y_{i,t}^{\tn{break}} \quad \forall i \in I \\
&D_i^{\tn{min}} \leq \sum{t \in T} y_{i,t}^{\tn{shift}} \leq D_i^{\tn{max}} \quad \forall i \in I
\end{align}

\end{document}