\be
\item Solve each of the LPs using the Big M Method.
		\be
        \item \begin{align*}
		\mbox{minimize } z &=-x_1+4x_2   \\
		\mbox{ subject to} \\
		x_1 +3x_2 &\geq 8 \\
		x_1+x_2 &\geq 4  \\
		x_1-x_2 &\leq 2  \\
		x_1,x_2 &\geq 0
		\end{align*}
		\item \begin{align*}
		\mbox{minimize } z &=x_1+x_2   \\
		\mbox{ subject to} \\
		2x_1 +3x_2 &\geq 30 \\
		-x_1+2x_2 &\leq 6  \\
		x_1+3x_2 &\geq 18  \\
		x_1,x_2 &\geq 0
		\end{align*}
		\item
		\begin{align*}
		\mbox{maximize } z &=x_1+5x_2 +6x_3  \\
		\mbox{ subject to} \\
		x_1+4x_2 +2x_3 &=50 \\
		x_1-4x_2 +4x_3 &\geq 40  \\
		x_1,x_2,x_3 &\geq 0
		\end{align*}
	\ee
\ee

