\documentstyle{article}

\addtolength{\topmargin}{-1cm}
\addtolength{\textheight}{2cm}
\addtolength{\textwidth}{3cm}
\addtolength{\oddsidemargin}{-1.5cm}

\newcommand{\nn}{\nonumber}
\newcommand{\beas}{\begin{eqnarray*}}
\newcommand{\eeas}{\end{eqnarray*}}
\newcommand{\bd}{\begin{displaymath}}
\newcommand{\ed}{\end{displaymath}}
\newcommand{\mb}{\mbox}
\newcommand{\ba}{\begin{array}}
\newcommand{\ea}{\end{array}}

\newcommand{\D}{\displaystyle}
\newcommand{\ol}{\overline}
\newcommand{\ul}{\underline}
\newcommand{\ti}{\tilde}
\newcommand{\bs}{\backslash}



\author{Teschl Gerald}
\title{Quiz 4}
\date{11 Sep. 1995}

\begin{document}

\thispagestyle{empty}

\hfill {\bf Name}: $\ul{\hspace*{5cm}}$\\[2mm]
\hspace*{2mm}\hfill {\bf ID \#}: $\ul{\hspace*{5cm}}$\\[5mm]

{\Huge Quiz 4}\\[5mm]

\noindent{\em Leontief production model}. The economy of a country is based on three
industries -- the electric company, water company, and steel company.
\begin{itemize}
\item To produce a certain amount of electricity the electric company needs the following:
5\% of its own electricity; water, worth 10\% of the value of its own electricity; steel,
worth 15\% of the value of its own electricity.
\item To produce a certain amount of water the water company needs the following:
electricity, worth 12\% of the value of its own water; 10\% of its own water; steel, worth
14\% of the value of its own water.
\item To produce a certain amount of steel the steel company
needs the following: electricity, worth 20\% of the value of its own steel; 20\% of its
own steel.
\end{itemize}
Find the value of the produced electricity, water and steel if the customers
demand 88 million dollars worth of electricity, 33 million dollars worth of water, and
55 million dollars worth of steel products.\\[3mm]
(a) Write down the {\em input-output matrix} $A$.~\hfill (5pts)\\[5.5cm]
(b) Compute the value of the electricity, water and steel produced.~\hfill (5pts)

\end{document}
