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2a geloest.

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Jim Martens 2013-10-15 15:46:36 +02:00
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optimierung/Uebungsblatt1.tex
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@ -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}