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\title{MA162: Finite mathematics}
\subtitle{Linear Programming:  More on the Simplex Algorithm}
\author{Paul Koester}
\institute{University of Kentucky}
\date{April 28, 2014}

\begin{document}

\maketitle

\begin{frame}{Linear Programming with the Simplex Algorithm, Ex 1}
\begin{itemize}
  \item[] Use the simplex algorithm to solve this LPP:
  \item[] Maximize:  \(P = 3x + 4y\) 
  \item[] Constraints: 
    \begin{itemize}
      \item \( x + y \leq 4\)
      \item \( 2x + y \leq 5\)
      \item \( x \geq 0, y \geq 0\)
    \end{itemize}
\end{itemize}
\end{frame}

\begin{frame}{Linear Programming with the Simplex Algorithm, Ex 2}
\begin{itemize}
  \item[] Use the simplex algorithm to solve this LPP:
  \item[] Maximize:  \(P = 3x + 4y + z\) 
  \item[] Constraints: 
    \begin{itemize}
      \item \( 3x + 10y + 5z \leq 120\)
      \item \( 5x +  2y + 8z \leq   6\)
      \item \( 8x + 10y + 3z \leq 105\)
      \item \( x \geq 0, y \geq 0, z \geq 0\)
    \end{itemize}
\end{itemize}
\end{frame}

\begin{frame}{Linear Programming with the Simplex Algorithm, Ex 3}
\begin{itemize}
  \item[] Boise Lumber manufactures prefabricated houses.  They offer three models, standard, deluxe, and luxury.
  \item[] Each house is prefabricated and partially assembled in a factory.  The final assembly is done on site. 
  \item[] The dollar amount of building material required, the amount of factory labor required, and the amount of on-site labor required, as 
          well as profit per unit are \\
          \begin{tabular}{lrrr} \hline
                         & Standard & Deluxe & Luxary \\ \hline
          Material       &     6000 &   8000 &  10000 \\ \hline
          Factory labor  &      240 &    220 &    200 \\ \hline
          On-site labor  &      180 &    210 &    300 \\ \hline
          Profit         &     3400 &   4000 &   5000 \\ \hline
          \end{tabular}
  \item[] They have \(\$8,200,000\) budgeted for building materials, \(218,000\) hours for factory labor, and \(237,000\) labor hours for 
          on-site labor.  
  \item[] How many houses of each type should they build in order to maximize their profit?
\end{itemize}
\end{frame}




\end{document}
