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\title{General Mathematics and CPS II}
\author{Exercise 17}
\date{April 15, 2015}
\maketitle

\begin{enumerate}
\item On the last homework, you wrote the following linear programming
problem in its standard form.

Maximize
\[
  z = 2 \, x_1 - x_2 + x_3
\]
subject to 
\begin{gather*}
  x_1 - x_2 \leq 1 \,, \\
  x_2 - x_3 \geq 1 \,, \\
  x_3 - x_1 \leq 3 \,, \\
  x_1 \geq -2 \,, \\
  x_2 \leq 1 \,, \\
  x_3 \leq 0 \,.
\end{gather*}

Now solve this LPP using the simplex method.

\item Show that the leaving variable in one iteration of the simplex
method can never be the entering variable in the next iteration.

\end{enumerate}

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