\beamer@endinputifotherversion {3.06pt}
\select@language {english}
\beamer@sectionintoc {2}{Graphical solutions to two dimensional problems}{6}{1}{1}
\beamer@subsectionintoc {2}{1}{Representing constraints as sections of the plane}{6}{1}{1}
\beamer@subsectionintoc {2}{2}{Handling the objective function}{19}{1}{1}
\beamer@subsectionintoc {2}{3}{Exercises}{31}{1}{1}
\beamer@sectionintoc {3}{Convexity and Polyhedral Sets}{65}{1}{2}
\beamer@subsectionintoc {3}{1}{Hyperplanes and Halfspaces}{65}{1}{2}
\beamer@subsectionintoc {3}{2}{Convexity and Polyhedral Sets}{68}{1}{2}
\beamer@sectionintoc {4}{Extreme Points and Extreme Directions}{76}{1}{3}
\beamer@subsectionintoc {4}{1}{Extreme Points}{76}{1}{3}
\beamer@subsectionintoc {4}{2}{Properties of Extreme points and Extreme directions}{81}{1}{3}
\beamer@subsectionintoc {4}{3}{Importance}{111}{1}{3}
\beamer@sectionintoc {5}{Basic Feasible Solutions}{126}{1}{4}
\beamer@subsectionintoc {5}{1}{Finding Basic Feasible Solutions}{126}{1}{4}
\beamer@subsectionintoc {5}{2}{Relation to Extreme Points}{136}{1}{4}