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\title{Operations Research}
\author{Homework 3}
\date{Due via Moodle or Mailbox on Tuesday, September 22, 2020}
\maketitle

\begin{enumerate}
\item Reconsider Problem~1 from Homework Set~1: \emph{Minimize}
\[
  z = 8 \, x + 12 \, y
\]
\emph{subject to}
\begin{gather*}
  5 \, x + 2 \, y \geq 20 \,, \\
  4 \, x + 3 \, y \geq 24 \,, \\
  y \geq 2 \,, \\
  x, y \geq 0 \,.
\end{gather*}

On Homework Set~2 Problem~3, you wrote this problem in standard form.

Now, solve the problem using the simplex method \emph{on paper}.
%% This is a bad problem for the simplex method.  Initialization must
%% be done ad hoc (possible) or via penalty variables (not yet done in
%% class).  Better replace by other problem next time!


\item \begin{enumerate}
\item Write a ``concrete'' Pyomo model to solve the same problem.  
\item How does the solution change if you ask for maximizing $z$
instead?
\end{enumerate}

You should submit a printout of your Ipython notebook which shows the
model setup and the computed solutions to (a) and (b).

\end{enumerate}

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