This is one of a series of three tests that constitute the exam of the course. The test consists of a number of tasks divided into subtasks. The answers must be collected in a unique PDF document and are to be handed in electronically in ItsLearning (to be confirmed)
The test is individual. You are not allowed to collaborate by any means with other persons.
Your answers will be assessed by the teacher, the instructor and an external censor. Moreover, the answers will be grouped by subtasks by an automated parser tool. Therefore, it is very important that you follow the instructions below.
Keep your answers anonymous but make sure that you specify your exam number. Use the Latex and Word templates provided in the external web page to see where to specify the exam number.
In the PDF document make sure that you start a new page for every SUBTASK and you write a section title that includes the word “Subtask”, specifying which SUBTASK you are addressing. Use the Latex and Word templates provided in the external web page.
You can write your answers in Danish or in English.
Remember to justify all your statements! It is not sufficient to present an answer, you must show how you found it. You may refer to results from the lecture notes, the slides or the books listed at the course web page. References to other books (outside the course material) or to internet links are not accepted as valid answers to a task.
You are allowed to use tools such as Python to assist you the calculations. If you report source code in Python or other languages, you must also report the output it produces when executed.
Make sure you take security copies of your documents while the test is in progress. It is your own responsibility in case of technical issues.
Tools and tutorials for types setting your answers are available from the Public Web Page:\ Assessment $\rightarrow$ Preparation for the take-home assignments. (This page below.)
The contribution to the final evaluation of each task, if carried out correctly, is given at the beginning of each task as a list of points for each subtask. The maximum total score is 100.
Digital pens and scanners.
Mathematical formulas, if not handwritten, are best encoded in LaTeX. Typesetting them in Word takes too long.
Python for matrix operations (modules “numpy” and “fractions”)
Alternatives to Python for matrix calculations: R, MATLAB, Maple, etc.
[WC] Stefan Waner and Steven R. Costenoble. Simplex Method tool
Text editor in VERBATIM mode (Unix: EMACS + ORG mode; Win: Gusek, etc)
Tools for plotting graphs: LP Grapher, grapher in Mac, graph.tk, tikz in Latex.
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{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}
\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}