\documentclass{uebungsblatt}
\author{Marek Kubica, kubica@in.tum.de}
\fach{Grundlagen Betriebssysteme}
\blatt{7}
\gruppe{22}
\usepackage{tikz}
\usetikzlibrary{topaths,decorations.markings}

\begin{document}

\aufgabe

\teilaufgabe

$P_3$ oben, $P_2$ in der mitte, $P_1$ unten:

\begin{tikzpicture}
  [scale=0.7]

  \draw (0,0) -- (0,4);
  \draw (0,0) -- (21,0);

  %p1
  \draw [dashed] (0,1) -- (2,1);
  \draw (2,1) -- (4,1);
  \draw [dashed] (4,1) -- (6,1);
  \draw [dashed] (6,1) -- (8,1);
  \draw (8,1) -- (10,1);
  \draw [dashed] (10,1) -- (12,1);
  \draw [dashed] (12,1) -- (14,1);
  \draw (14,1) -- (16,1);

  %p2
  \draw [dashed] (2,2) -- (4,2);
  \draw [dashed] (4,2) -- (6,2);
  \draw (6,2) -- (8,2);
  \draw [dashed] (8,2) -- (10,2);
  \draw [dashed] (10,2) -- (12,2);
  \draw (12,2) -- (14,2);
  \draw [dashed] (14,2) -- (16,2);
  \draw [dashed] (16,2) -- (18,2);
  \draw (18,2) -- (20,2);
  
  %p3
  \draw (0,3) -- (2,3);
  \draw [dashed] (2,3) -- (4,3);
  \draw (4,3) -- (6,3);
  \draw [dashed] (6,3) -- (8,3);
  \draw [dashed] (8,3) -- (10,3);
  \draw (10,3) -- (12,3);
  \draw [dashed] (12,3) -- (14,3);
  \draw [dashed] (14,3) -- (16,3);
  \draw (16,3) -- (18,3);

\end{tikzpicture}

\teilaufgabe

\begin{align*}
c_1& = 16&
  a_1& = 0&
  b_1& = 6&
  v_1& = 16&
  w_1& = 10\\
c_2& = 20&
  a_2&= 2&
  b_2& = 6&
  v_2& = 18&
  w_2& = 12\\
c_3& = 18&
  a_3& = 0&
  b_3& = 8&
  v_3& = 18&
  w_3& = 10
\end{align*}

\begin{align*}
\overline{V}& = \frac{1}{3}(16 + 18 + 18) = 17 \frac{1}{3}\\
\overline{W}& = \frac{1}{3}(10 + 12 + 10) = 10 \frac{2}{3}
\end{align*}

\end{document}
