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\begin{document}

\begin{center}
{\Large Worksheet}
\end{center}


The following simplex matrices are from a maximization problem that was set up
as in section~3.4.
I have also performed task B.
\begin{itemize}
\item  Identify the constraints and the objective function that I started with.
\item  Identify the solution.
\item  Go through task B and make sure your answer matches up with mine.
\end{itemize}
\begin{enumerate}
\item 
\[
\left[
\begin{array}{rrrrrr|r}
3 & 1 & 1 & 1 & 0 & 0 & 100 \\
4 & 3 & 6 & 0 & 1 & 0 & 250 \\
\hline
-5 & -3 & -4 & 0 & 0 & 1 & 0
\end{array}
\right]
\longrightarrow
\left[
\begin{array}{rrrrrr|r}
1 & 0 & -3/5 & 3/5 & -1/5 & 0 & 10 \\
0 & 1 & 14/5 & -4/5 & 3/5 & 0 & 70 \\
\hline
0 & 0 & 7/5 & 3/5 & 4/5 & 1 & 260
\end{array}
\right]
\]

\item  
\[
\left[
\begin{array}{rrrrrrr|r}
5 & 5 & 7 & 1 & 0 & 0 & 0 & 12 \\
4 & 0 & 6 & 0 & 1 & 0 & 0 & 48 \\
0 & 1 & 1 & 0 & 0 & 1 & 0 & 8 \\
\hline
-1 & -3 & -1 & 0 & 0 & 0 & 1 & 0
\end{array}
\right]
\longrightarrow
\left[
\begin{array}{rrrrrrr|r}
1  & 1 & 7/5  & 1/5  & 0 & 0 & 0 & 12/5 \\
4  & 0 & 6    & 0    & 1 & 0 & 0 & 48 \\
-1 & 0 & -2/5 & -1/5 & 0 & 1 & 0 & 28/5 \\
\hline
2  & 0 & 16/5 & 3/5  & 0 & 0 & 1 & 36/5
\end{array}
\right]
\]

\item  
\[
\left[
\begin{array}{rrrrr|r}
14 & 14 & 1 & 0 & 0 & 98 \\
 8 & 10 & 0 & 1 & 0 & 100 \\
\hline
-7 & -10 & 0 & 0 & 1 & 0 
\end{array}
\right]
\longrightarrow
\left[
\begin{array}{rrrrr|r}
1 & 1 & 1/14 & 0 & 0 & 7 \\
-2 & 0 & -5/14 & 1 & 0 & 30 \\
\hline
3 & 0 & 5/7 & 0 & 1 & 70 \\
\end{array}
\right]
\]

\item  
\[
\left[
\begin{array}{rrrrrr|r}
2 & 5 & 1 & 0 & 0 & 0 & 30 \\
1 & 5 & 0 & 1 & 0 & 0 & 25 \\
1 & 1 & 0 & 0 & 1 & 0 & 11 \\
\hline
-2 & -6 & 0 & 0 & 0 & 1 & 0
\end{array}
\right]
\longrightarrow
\left[
\begin{array}{rrrrrr|r}
1 & 0 &    1 &  -1 & 0 & 0 & 5 \\
0 & 1 & -1/5 & 2/5 & 0 & 0 & 4 \\
0 & 0 & -4/5 & 3/5 & 1 & 0 & 2 \\
\hline
0 & 0 &  4/5 & 2/5 & 0 & 0 & 34 
\end{array}
\right]
\]

\item  
\[
\left[
\begin{array}{rrrrrrr|r}
4 & 2  & 2 & 1 & 0 & 0 & 0 & 40 \\
8 & 10 & 5 & 0 & 1 & 0 & 0 & 90 \\ 
4 & 4  & 3 & 0 & 0 & 1 & 0 & 30 \\
\hline
-64 & -36 & -38 & 0 & 0 & 0 & 1 & 0
\end{array}
\right]
\longrightarrow
\left[
\begin{array}{rrrrrrr|r}
0 & -2 & -1 &  1 & 0 & -1 & 0 & 10 \\
0 &  2 & -1 &  0 & 1 & -2 & 0 & 30 \\
1 &  1 & 3/4 & 0 & 0 & 1/4 & 0 & 15/2 \\
\hline
0 & 28 & 10  & 0 & 0 & 16 & 1 & 480
\end{array}
\right]
\]

\item  
\[
\left[
\begin{array}{rrrrrrr|r}
2 & 1 & 1 & 1 & 0 & 0 & 0 & 50 \\
1 & 3 & 0 & 0 & 1 & 0 & 0 & 20 \\
0 & 1 & 1 & 0 & 0 & 1 & 0 & 15 \\
\hline
-10 & -5 & -4 & 0 & 0 & 0 & 1 & 0
\end{array}
\right]
\longrightarrow
\left[
\begin{array}{rrrrrrr|r}
0 & -5 & 1 &  1 & -2 & 0 & 0 & 10 \\
1 &  3 & 0 &  0 &  1 & 0 & 0 & 20 \\
0 &  6 & 0 & -1 &  2 & 1 & 0 & 5  \\
\hline
0 &  5 & 0 &  4 &  2 & 0 & 1 & 240 \\
\end{array}
\right]
\]











\end{enumerate}


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