95 lines
1.9 KiB
TeX
95 lines
1.9 KiB
TeX
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\documentclass[a4paper, 12pt]{article}
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\newcommand{\bold}{\textbf}
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\usepackage[english]{babel}
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\usepackage{amsmath}
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\usepackage{tikz}
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\usepackage{indentfirst}
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\begin{document}
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\newcommand{\q2}{\quad\quad}
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\title{\Large{\bold{Moontorio}}}
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\author{Matei Adriel}
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\date {}
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\maketitle
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\section{Example 1}
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Solve the following factory:
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\vspace*{20pt}
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\begin{figure}[h]
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\centering
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\begin{tikzpicture}[shorten >=1pt, auto, node distance={30mm},
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main/.style = {draw, rectangle}]
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\node[main] (3) {$consumer_1$};
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\node[main] (1) [above left of=3] {$provider_1$};
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\node[main] (2) [below left of=3] {$provider_2$};
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\node[main] (4) [right of=2] {$consumer_2$};
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\draw[->] (1) edge node{$p_1$} (3);
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\draw[->] (2) edge node{$p_2$} (3);
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\draw[->] (2) edge node{$p_3$} (4);
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\end{tikzpicture}
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\caption{Factory}
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\label{fig:Factory}
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\end{figure}
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Generating the constraints:
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\begin{figure}[h]
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\centering
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\begin{equation}
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p_1(t) < provider_1(t)
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\end{equation}
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\begin{equation}
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p_3(t) < consumer_2(t)
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\end{equation}
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\begin{equation}
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\begin{split}
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\begin{cases}
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\begin{cases}
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p_2(t) &< \displaystyle\frac{consumer_1(t)}{2}\\
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p_1(t) &< consumer_1(t) - p_2(t)
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\end{cases}
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\ ,&\;\mbox{if } p_1(t) \geq p_2(t)\\\\
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\begin{cases}
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p_1(t) &< \displaystyle\frac{consumer_1(t)}{2}\\
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p_2(t) &< consumer_1(t) - p_1(t)
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\end{cases}
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\ ,&\;\mbox{if } p_1(t) < p_2(t)
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\end{cases}
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\end{split}
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\end{equation}
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\begin{equation}
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\begin{split}
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\begin{cases}
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\begin{cases}
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p_3(t) &< \displaystyle\frac{provider_2(t)}{2}\\
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p_2(t) &< provider_2(t) - p_3(t)
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\end{cases}
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\ ,&\;\mbox{if } p_2(t) \geq p_3(t)\\\\
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\begin{cases}
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p_2(t) &< \displaystyle\frac{provider_2(t)}{2}\\
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p_3(t) &< provider_2(t) - p_3(t)
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\end{cases}
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\ ,&\;\mbox{if } p_2(t) < p_3(t)
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\end{cases}
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\end{split}
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\end{equation}
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\caption{Constraints}
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\label{fig:Constraints}
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\end{figure}
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\end{document}
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