Notes

documentclass[12pt]{beamer}
usetheme{Madrid}
usepackage[utf8]{inputenc}
usepackage{amsmath}
usepackage{amsfonts}
usepackage{amssymb}
usepackage{graphicx}
title{INTEGER PROGRAMMING PROBLEM}
author{Prof. M.K. CHAUDHARY}
institute{Department of Statistics \Institute of Science\ Banaras Hindu University}
date{}
%setbeamercovered{transparent}
%setbeamertemplate{navigation symbols}{}
%logo{includegraphics[scale=0.25]{BHU.jpeg}}
%institute{}
%date{}
%subject{}
begin{document}


begin{frame}
maketitle
end{frame}

%begin{frame}
%tableofcontents
%end{frame}
begin{frame}{Linear Programming model}
In a general linear programming model, all the decision variables can take only non-negative continuous value in the solution i.e. they can be assigned any non-negative integer as well as fractional value. However, there are certain practical problems in which the fractional value of the decision variables has no significance. The integer solution to a problem can, however, be obtained by rounding off the optimum values of the variables to the nearest integer values. This approach can be easy in terms of economy of effort, time and cost that might be required to derive an integer solution but this solution may not satisfy all the given constraints. Secondly, the value of the objective function so obtained may differ from the original optimum value. All such difficulties can be avoided if the given problem where an integer solution is required, is solved by integer programming techniques.
end{frame}


section{Methods}
begin{frame}{Methods in LPP}
begin{itemize}
item Graphical method
item Simplex method
end{itemize}
end{frame}


begin{frame}
Salabh
begin{thebibliography}{99}
bibitem{article1}Author
emph{Title}
journal
end{thebibliography}
end{frame}

begin{frame}{}
begin{center}
Huge{Thanks!}
end{center}
end{frame}


end{document}