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MATH2-Inf-8: Blatt 8 korrigiert.

This commit is contained in:
Jim Martens 2013-12-16 20:31:50 +01:00
parent 300490a93b
commit 2b0d06f6ea
1 changed files with 7 additions and 7 deletions
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14
optimierung/Uebungsblatt8.tex
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@ -117,8 +117,8 @@ Stephan Niendorf (6242417)}
\frac{4}{5}x_{1} \,&=&&\, 20 + \frac{1}{50}x_{4} - x_{3} \\
x_{1} \,&=&&\, 25 + \frac{1}{40}x_{4} - \frac{5}{4}x_{3} \\
x_{2} \,&=&&\, 80 - \frac{1}{5}\left(25 + \frac{1}{40}x_{4} - \frac{5}{4}x_{3}\right) - \frac{1}{50}x_{4} \\
&=&&\, 80 - 5 + \frac{1}{200}x_{4} - \frac{1}{4}x_{3} - \frac{1}{50}x_{4} \\
&=&&\, 75 - \frac{3}{200}x_{4} - \frac{1}{4}x_{3} \\
&=&&\, 80 - 5 - \frac{1}{200}x_{4} + \frac{1}{4}x_{3} - \frac{1}{50}x_{4} \\
&=&&\, 75 - \frac{1}{40}x_{4} + \frac{1}{4}x_{3} \\
z \,&=&&\, 5600 + 26\left(25 + \frac{1}{40}x_{4} - \frac{5}{4}x_{3}\right) - \frac{7}{5}x_{4} \\
&=&&\, 5600 + 650 + \frac{13}{20}x_{4} - \frac{65}{2}x_{3} - \frac{7}{5}x_{4} \\
&=&&\, 6250 - \frac{3}{4}x_{4} - \frac{65}{2}x_{3}
@ -127,7 +127,7 @@ Stephan Niendorf (6242417)}
\underline{Ergebnis der 2. Iteration}:
\begin{alignat*}{4}
x_{1} \,&=&\, 25 \,&-&\, \frac{1}{40}x_{4} \,&-&\, \frac{5}{4}x_{3} \\
x_{2} \,&=&\, 75 \,&-&\, \frac{3}{200}x_{4} \,&-&\, \frac{1}{4}x_{3} \\ \cline{1 - 7}
x_{2} \,&=&\, 75 \,&-&\, \frac{1}{40}x_{4} \,&+&\, \frac{1}{4}x_{3} \\ \cline{1 - 7}
z &=& 6250 \,&-&\, \frac{3}{4}x_{4} \,&-&\, \frac{65}{2}x_{3}
\end{alignat*}
@ -242,8 +242,8 @@ Stephan Niendorf (6242417)}
\frac{4}{5}x_{1} \,&=&&\, 20 - \frac{1}{50}t + \frac{1}{50}x_{4} - x_{3} \\
x_{1} \,&=&&\, 25 - \frac{1}{40}t + \frac{1}{40}x_{4} - \frac{5}{4}x_{3} \\
x_{2} \,&=&&\, 80 + \frac{1}{50}t - \frac{1}{5}\left(25 - \frac{1}{40}t + \frac{1}{40}x_{4} - \frac{5}{4}x_{3}\right) - \frac{1}{50}x_{4} \\
&=&&\, 80 + \frac{1}{50}t - 5 + \frac{1}{200}t - \frac{1}{200}x_{4} - \frac{1}{4}x_{3} - \frac{1}{50}x_{4} \\
&=&&\, 75 + \frac{1}{40}t - \frac{1}{40}x_{4} - \frac{1}{4}x_{3} \\
&=&&\, 80 + \frac{1}{50}t - 5 + \frac{1}{200}t - \frac{1}{200}x_{4} + \frac{1}{4}x_{3} - \frac{1}{50}x_{4} \\
&=&&\, 75 + \frac{1}{40}t - \frac{1}{40}x_{4} + \frac{1}{4}x_{3} \\
z \,&=&&\, 5600 + \frac{7}{5}t + 26\left(25 - \frac{1}{40}t + \frac{1}{40}x_{4} - \frac{5}{4}x_{3}\right) - \frac{7}{5}x_{4} \\
&=&&\, 5600 + \frac{7}{5}t + 650 - \frac{13}{20}t + \frac{13}{20}x_{4} - \frac{65}{2}x_{3} - \frac{7}{5}x_{4} \\
&=&&\, 6250 + \frac{3}{4}t - \frac{3}{4}x_{4} - \frac{65}{2}x_{3}
@ -251,8 +251,8 @@ Stephan Niendorf (6242417)}
\underline{Ergebnis der 2. Iteration}:
\begin{alignat*}{4}
x_{1} \,&=&\, 25 - \frac{1}{40}t \,&-&\, \frac{1}{40}x_{4} \,&-&\, \frac{5}{4}x_{3} \\
x_{2} \,&=&\, 75 + \frac{1}{40}t \,&-&\, \frac{1}{40}x_{4} \,&-&\, \frac{1}{4}x_{3} \\ \cline{1 - 7}
x_{1} \,&=&\, 25 - \frac{1}{40}t \,&+&\, \frac{1}{40}x_{4} \,&-&\, \frac{5}{4}x_{3} \\
x_{2} \,&=&\, 75 + \frac{1}{40}t \,&-&\, \frac{1}{40}x_{4} \,&+&\, \frac{1}{4}x_{3} \\ \cline{1 - 7}
z &=& 6250 + \frac{3}{4}t \,&-&\, \frac{3}{4}x_{4} \,&-&\, \frac{65}{2}x_{3}
\end{alignat*}