Solve each of the following LPs using the revised simplex algorithm.
	\be
	\item
		\begin{align*}
		 \mbox{maximize } z &=3x_1+2x_2  \\
		\mbox{ subject to} \notag\\
		x_1 \phantom{ +20x_2} &\leq 4 \notag\\
		x_1+3x_2 &\leq 15  \notag\\
		2x_1+x_2 &\leq 10 \notag \\
		x_1,x_2 &\geq 0\notag
		\end{align*}	
	
	\item
		\begin{align*}
		 \mbox{maximize } z &=4x_1 + x_2 +5x_3  \\
		\mbox{ subject to} \\
		2x_1+x_2+3x_3 &\leq 14 \\
		6x_1+3x_2 +3x_3 &\leq 22  \\
		2x_1+3x_2  \x &\leq 14  \\
		x_1,x_2,x_3 &\geq 0
		\end{align*}	
	\item
		\begin{align*}
		\mbox{minimize } z &=3x_1-2x_2   \\
		\mbox{ subject to} \\
		x_1 -2x_2 &\leq 2 \\
		x_1+x_2 &\leq 4  \\
		x_1,x_2 &\geq 0
		\end{align*}
	\ee
