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\begin{document}
\noindent Name: \rule{7cm}{.2pt} \vspace{.3cm} \hfill Date:  \rule{3.5cm}{.2pt}
\vspace{.3cm}

\noindent\hrulefill
\begin{center}
{\bf \Large{MA 162}} \\\vspace{.1cm} Week 9 Recitation Worksheet (Thursday)
\end{center}
\vspace{-.3cm}
\hrulefill

\begin{center}
\fbox{\textbf{You must show all work to receive full credit.}}
\end{center}

\begin{enumerate}[ref=\#\arabic*]
%1
\item Graph the feasible region for the following system of inequalities.
$$\left\{\begin{array}{rcr} 2x+3y & \le & 12 \\ x-y & \ge & -1 \\ x & \ge & 0 \\ y & \ge & 0  \end{array}\right.$$
\begin{center}
	\begin{tikzpicture}[scale=1]
			\draw[help lines] (-1.5,-1.5) grid (6.5,6.5);
			\draw[ultra thick,<->] (-2,0) -- (7,0) node[right] {$x$};
			\draw[ultra thick,<->] (0,-2) -- (0,7) node[above] {$y$};
			\foreach \x in {1,2,...,6} { \draw[thick] ( \x,0.2) -- ( \x,-0.2) ( \x,0) +(0,-0.10) node[below] {$\x$}; }
			\foreach \y in {1,2,...,6} { \draw[thick] (0.2, \y) -- (-0.2, \y) (0, \y) +(-0.10,0) node[left]  {$ \y$}; }
			\foreach \x in {1} { \draw[thick] (-\x,0.2) -- (-\x,-0.2) (-\x,0) +(0,-0.10) node[below] {$-\x$}; }
			\foreach \y in {1} { \draw[thick] (0.2,-\y) -- (-0.2,-\y) (0,-\y) +(-0.10,0) node[left]  {$-\y$}; }

			%\node[circle,inner sep=2pt,fill=black,label=right:{$(\hspace{0.75cm},\hspace{0.75cm})$}] at (4,3) {};
			%\node[circle,inner sep=2pt,fill=black,label=left:{$(\hspace{0.75cm},\hspace{0.75cm})$}] at (-5,4) {};
			%\node[circle,inner sep=2pt,fill=black,label=left:{$(\hspace{0.75cm},\hspace{0.75cm})$}] at (-2,-5) {};
			%\node[circle,inner sep=2pt,fill=black,label=right:{$(\hspace{0.75cm},\hspace{0.75cm})$}] at (3,-2) {};
	\end{tikzpicture}
\end{center}
\vspace{1cm}

Determine the corner point(s) of the feasible region.


\newpage
%2
\item Graph the feasible region for the following system of inequalities.
$$\left\{\begin{array}{rcr} 2x-y & \le & -2 \\ 3x+5y & \ge & 15 \\ x & \ge & 0 \\ y & \ge & 0  \end{array}\right.$$
\begin{center}
	\begin{tikzpicture}[scale=1]
			\draw[help lines] (-1.5,-1.5) grid (6.5,6.5);
			\draw[ultra thick,<->] (-2,0) -- (7,0) node[right] {$x$};
			\draw[ultra thick,<->] (0,-2) -- (0,7) node[above] {$y$};
			\foreach \x in {1,2,...,6} { \draw[thick] ( \x,0.2) -- ( \x,-0.2) ( \x,0) +(0,-0.10) node[below] {$\x$}; }
			\foreach \y in {1,2,...,6} { \draw[thick] (0.2, \y) -- (-0.2, \y) (0, \y) +(-0.10,0) node[left]  {$ \y$}; }
			\foreach \x in {1} { \draw[thick] (-\x,0.2) -- (-\x,-0.2) (-\x,0) +(0,-0.10) node[below] {$-\x$}; }
			\foreach \y in {1} { \draw[thick] (0.2,-\y) -- (-0.2,-\y) (0,-\y) +(-0.10,0) node[left]  {$-\y$}; }

			%\node[circle,inner sep=2pt,fill=black,label=right:{$(\hspace{0.75cm},\hspace{0.75cm})$}] at (4,3) {};
			%\node[circle,inner sep=2pt,fill=black,label=left:{$(\hspace{0.75cm},\hspace{0.75cm})$}] at (-5,4) {};
			%\node[circle,inner sep=2pt,fill=black,label=left:{$(\hspace{0.75cm},\hspace{0.75cm})$}] at (-2,-5) {};
			%\node[circle,inner sep=2pt,fill=black,label=right:{$(\hspace{0.75cm},\hspace{0.75cm})$}] at (3,-2) {};
	\end{tikzpicture}
\end{center}
\vspace{1cm}

Determine the corner point(s) of the feasible region.


\end{enumerate}
\end{document}