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\title{General Mathematics and CPS II}
\author{Exercise 15}
\date{April 2, 2014}
\maketitle

\begin{enumerate}

\item (From Lial \emph{et al.}) Solve the following linear programming
problem: Maximize
\[
  z = 4 \, x + 2 \, y
\]
subject to 
\begin{gather*}
  x + y \leq 5 \,, \\
  2 \, x + y \geq 2 \,, \\
  x + 2 \, y \geq 3 \,, \\
  x \geq 0 \,, \\
  y \geq 0 \,.
\end{gather*}

\item (From Lial \emph{et al.}) A farming community owns 2 acres of
land and can afford to devote 40 days a year to harvesting.  Two crops
can be grown in the region, millet and wheat, which produce
$200\,\text{kg}$ and $400\,\text{kg}$ per acre, respectively.  Millet
requires $10$ days per acre to harvest, while wheat requires $30$ days
per acre.  How many acres should be devoted to each crop to maximize
the weight of grain harvested?



\end{enumerate}

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