DM545/DM871 -- Linear and Integer Programming

• The exam is digital. To digitalize handwritten text, formulas and graphs digital pen or hand scanner (that is, a silent scanner) are allowed.

• Recommended answer templates
  • Latex (PDF) | Word | OpenDocument

• 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.

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.
  • Latex symbol classifier
  • Syntax Highlight Code In Word Documents
• Python can be used with your own favourite Integrated Development Environment. Alternatively, you can use "Spyder" that comes with the "Anaconda" distribution or Jupyter.
  • Python for matrix operations (modules "numpy" and "fractions")

• 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{equation}
\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}
\end{equation}

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

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