\documentstyle[12pt,fullpage]{article}
\begin{document}
\begin{center}
{\Large \bf C\&O 370} \\
{\Large \bf HOMEWORK 1}
\end{center}
\medskip
Due: Friday, September 29, 1995 Sect. 1, 
Thursday, September 28, 1995 Sect. 2

\medskip
\noindent
{\bf Reading} \\
\begin{tabular}{lll}
Chapter 2 & (pp. 48-83) & Solving Linear Programs \\
Chapter 4 & (pp. 157-181) & Duality Thoery  \\
Appendix B & (pp. 690-703) & Linear Programming in Matrix Form
\end{tabular}

\bigskip
\noindent
{\bf Problems}
\begin{enumerate}
\item[1.1.]
Solve the product mix problem given in class using MATLAB to implement the
revised simplex
method refined by Bland's pivot rule.
\item[1.2.]
Consider the following linear program:
\[ \begin{array}{lllcrcrcl}
(P) & \mbox{maximize} & z & = & 3x_{1} & - & 4x_{2} & & \\
 & \mbox{subject to} & & & x_{1} & + & 2x_{2} & \geq & 2 \\
& & & & 3x_{1} & + & x_{2} & \geq & 4 \\
& & & & x_{1} & - & x_{2} & \leq & 1 \\
& & & & x_{1} & + & x_{2} & \leq & 3 \\
& & & & x_{1} & & & \geq & 0 \\
& & & & & & x_{2} & \geq & 0.
\end{array} \]
\begin{itemize}
\item[(a)]
Solve (P) using MATLAB to implement the (two-phase) revised simplex method
refined by Bland's rule.
\item[(b)]
Solve (P) using MATLAB to implement the criss-cross method refined by
Bland's rule.
\item[(c)]
Verify the optimality of your solution to (P).
\end{itemize}
\end{enumerate}
\bigskip
\noindent
{\bf Case Study \#1.}  Do \#10, pp. 35-36 of text.
\end{document}






