\relax 
\citation{goemans:lp}
\citation{karloff:lp}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}}
\@writefile{toc}{\contentsline {section}{\numberline {2}The Diet Problem}{1}}
\newlabel{sec:lec.lp}{{2}{1}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Knapsack Problem}{2}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Minimum Spanning Tree Problem}{2}}
\@writefile{toc}{\contentsline {section}{\numberline {3}Equivalent Forms}{3}}
\newlabel{sec:form}{{3}{3}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}General Form}{3}}
\newlabel{sec:form:gen}{{3.1}{3}}
\newlabel{eqn:gen:sum}{{1}{3}}
\newlabel{eqn:gen:mat}{{2}{3}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Standard Form}{4}}
\newlabel{sec:form:can}{{3.2}{4}}
\newlabel{eqn:can:sum}{{3}{4}}
\newlabel{eqn:can:mat}{{4}{4}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Slack Form}{4}}
\newlabel{sec:form:std}{{3.3}{4}}
\newlabel{eqn:std:sum}{{5}{4}}
\newlabel{eqn:std:mat}{{6}{4}}
\newlabel{def:feasible}{{1}{4}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.4}Constraint Conversion}{5}}
\@writefile{toc}{\contentsline {section}{\numberline {4}Example}{5}}
\newlabel{sec:example}{{4}{5}}
\newlabel{ex:one}{{1}{5}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Feasible Region}}{6}}
\newlabel{fig:inequal}{{1}{6}}
\@writefile{toc}{\contentsline {section}{\numberline {5}The Geometry of LP}{6}}
\newlabel{sec:geometry}{{5}{6}}
\newlabel{def:polytope}{{2}{6}}
\newlabel{def:convex}{{3}{6}}
\newlabel{def:vertex}{{4}{6}}
\newlabel{thm:vertex}{{1}{6}}
\@writefile{toc}{\contentsline {section}{\numberline {6}Simplex Algorithm}{8}}
\newlabel{sec:lec7.simplex}{{6}{8}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.1}Pivoting}{8}}
\newlabel{ex:two}{{2}{8}}
\newlabel{eqn:one}{{7}{10}}
\newlabel{eqn:two}{{8}{10}}
\newlabel{eqn:three}{{9}{10}}
\newlabel{eqn:four}{{10}{10}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.2}Tableau Method}{11}}
\newlabel{ex:three}{{3}{11}}
\bibstyle{alpha}
\bibdata{/home/rraj/tex/bibtex/refs}
\bibcite{goemans:lp}{Goe94}
\bibcite{karloff:lp}{Kar91}
