# DM545/DM871 -- Linear and Integer Programming

## Guidelines

• The exam is digital. To digitalize handwritten text, formulas and graphs digital pen or hand scanner (that is, a silent scanner) are allowed.
• You can write your answers as you prefer in Danish or in English. Choose the language with which you are faster.
• If you report Python code, you must also report the output it produces when executed.
• Make sure that you make periodic backup copies of your documents during the exam. It is your own responsability in case of technical issues.

## Tools for digitalizing solutions

Being acquainted with some of these tools (or their equivalent in your system) would help you to digitalize your solutions more easily and faster:

• Digital pens, hand scanners.
• Mathematical formulas, if not handwritten, are best encoded in LaTeX. Typesetting them in Word takes too long.
• Python can be used with your own favourite Integrated Development Environment. Alternatively, you can use "Spyder" that comes with the "Anaconda" distribution or Jupyter.
• Alternatives to Python for matrix calculations: R, MATLAB, Maple, etc.
• Text editor in VERBATIM mode (Unix: EMACS + ORG mode; Win: Gusek, etc)
• Tools to plot graphs: LP Grapher, grapher in Mac, graph.tk, tikz in Latex.
• Danish-English Dictionary
• To write ILP models in Latex you can use one of the following templates:

\begin{align} \label{ob} \max \; \quad & \sum_{j=1}^nc_jx_j \\ \label{c1} \mbox{s.t.} \quad &\sum\limits_{j=1}^n a_{ij}x_j\geq b_i, \quad i=1,\ldots,m \\ \label{c2} &x_j \geq 0, \quad j=1,\ldots,n \end{align}

\begin{align}
\label{ob} \max \; \quad & \sum_{j=1}^nc_jx_j  \\
\label{c1} \mbox{s.t.} \quad &\sum\limits_{j=1}^n a_{ij}x_j\geq b_i,
\quad i=1,\ldots,m \\
\label{c2}   &x_j \geq 0, \quad j=1,\ldots,n
\end{align}

$$\begin{array}{lrll} \max & \sum\limits_{j=1}^nc_jx_j\\ &\sum\limits_{j=1}^n a_{ij}x_j&\leq b_i,& i=1,\ldots,m\\ &x_j&\geq 0,& j=1,\ldots,n \end{array}$$
$$\begin{array}{lrll} \max & \sum\limits_{j=1}^nc_jx_j\\ &\sum\limits_{j=1}^n a_{ij}x_j&\leq b_i,& i=1,\ldots,m\\ &x_j&\geq 0,& j=1,\ldots,n \end{array}$$


$\max \sum_{j=1}^nc_jx_j$ $\sum_{j=1}^n a_{ij}x_j\leq b_i, i=1,\ldots,m$ $x_j\geq 0, j=1,\ldots,n$

$$\label{ob} \max \sum_{j=1}^nc_jx_j\\$$
$$\label{c1} \sum_{j=1}^n a_{ij}x_j\leq b_i, i=1,\ldots,m\\$$
$$\label{c2} x_j\geq 0, j=1,\ldots,n$$


Created: 2020-02-11 Tue 18:43

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