From fc3746c63c946b35d0262ba2a38824585167a4f5 Mon Sep 17 00:00:00 2001
From: Jim Martens <jim1@live.de>
Date: Tue, 15 Oct 2013 15:46:36 +0200
Subject: [PATCH] 2a geloest.

---
 optimierung/Uebungsblatt1.tex | 27 +++++++++++++++++++++++++++
 1 file changed, 27 insertions(+)

diff --git a/optimierung/Uebungsblatt1.tex b/optimierung/Uebungsblatt1.tex
index 0810959..240bd15 100644
--- a/optimierung/Uebungsblatt1.tex
+++ b/optimierung/Uebungsblatt1.tex
@@ -58,5 +58,32 @@
 	\subsection{} %b
 \section{} %2
 	\subsection{} %a
+	Pauls Diätproblem:\\
+	\begin{alignat*}{7}
+		\text{maximiere}\; -& 3x_{1} &-& 24x_{2} &-& 13x_{3} &-& 9x_{4} &-& 20x_{5} &-& 19x_{6} && \\
+		\multicolumn{14}{l}{\text{unter den Nebenbedingungen}} && \\
+		- & 110x_{1} &-& 205x_{2} &-& 160x_{3} &-& 160x_{4} &-& 420x_{5} &-& 260x_{6} &\leq & -2000 \\
+		-& 4x_{1} &-& 32x_{2} &-& 13x_{3} &-& 8x_{4} &-& 4x_{5} &-& 14x_{6} &\leq & -55 \\
+		-& 2x_{1} &-& 12x_{2} &-& 54x_{3} &-& 285x_{4} &-& 22x_{5} &-& 80x_{6} &\leq & -800 \\
+		& x_{1} && && && && && &\leq &\, 4 \\
+		& && x_{2} && && && && &\leq &\, 3 \\
+		& && && x_{3} && && && &\leq &\, 2 \\
+		& && && && x_{4} && && &\leq &\, 8 \\
+		& && && && && x_{5} && &\leq &\, 2 \\
+		& && && && && && x_{6} &\leq &\, 2 \\
+		\multicolumn{12}{r}{$x_{1}, x_{2}, x_{3}, x_{4}, x_{5}, x_{6}$} \,&\geq &\, 0
+		\end{alignat*}
+		Problem (1.2) in Standardform:\\
+		\begin{alignat*}{7}
+		\text{maximiere}\; & 3x_{1}^{'} &-& 3x_{1}^{''} &+& x_{2} && && && \\
+		\multicolumn{14}{l}{\text{unter den Nebenbedingungen}} && \\
+		& x_{1}^{'} &-& x_{1}^{''} &-& 6x_{2} &+& x_{3} &-& x_{4}^{'} &+& x_{4}^{''} &\leq &\, 3 \\
+		& && && 7x_{2} && &-& 2x_{4}^{'} &+& 2x_{4}^{''} &\leq &\, 5 \\
+		& && &-& 7x_{2} && &+& 2x_{4}^{'} &-& 2x_{4}^{''} &\leq & -5 \\
+		-& x_{1}^{'} &+& x_{1}^{''} &+& x_{2} &+& x_{3} && && &\leq &\, 1 \\
+		& x_{1}^{'} &-& x_{1}^{''} &-& x_{2} &-& x_{3} && && &\leq & -1 \\
+		& && && && x_{3} &-& x_{4}^{'} &+& x_{4}^{''} &\leq &\, 2 \\
+		\multicolumn{12}{r}{$x_{1}^{'}, x_{1}^{''}, x_{2}, x_{3}, x_{4}^{'}, x_{4}^{''}$} \,&\geq &\, 0
+		\end{alignat*}
 	\subsection{} %b
 \end{document}