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\title{Operations Research}
\author{Homework 1}
\date{Due via Moodle on Tuesday, September 8, 2020}
\maketitle

\begin{enumerate}

\item Minimize
\[
  z = 8 \, x + 12 \, y
\]
subject to 
\begin{gather*}
  5 \, x + 2 \, y \geq 20 \,, \\
  4 \, x + 3 \, y \geq 24 \,, \\
  y \geq 2 \,, \\
  x, y \geq 0 \,.
\end{gather*}

\item A sum of $\$12\,000$ is to be invested.  At least half the
amount will go into an investment earning $6\%$ annual interest, but
involving some risk.  Thus, the amount in the risky investment may not
be more than three times the amount in a second, relatively riskless
investment earning $5\%$ annual interest.  How much should be invested
into each in order to maximize interest?

\end{enumerate}

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