
	Use the Cutting Plane Algorithm to solve each of the following ILPs.
		\be
		\item
		\begin{align*}
		 \mbox{maximize } z &=2x_1+3x_2  \\
		\mbox{ subject to} \notag\\
		4x_1 + 3x_2 &\leq 8 \notag\\
		2x_1+x_2 &\leq 15 \notag\\
        x_1+2x_2 &\leq 7 \notag\\
		x_1,x_2 &\geq 0, x_1,x_2 \in \Z \notag
		\end{align*}	
		\item
		\begin{align*}
		 \mbox{maximize } z &= 4x_1 + 3x_2 + 5x_3  \\
		\mbox{ subject to} \notag\\
		x_1+x_2+x_3  &\leq 17 \notag\\
		6x_1+3x_2+3x_3  &\leq 22 \notag\\
        3x_1+3x_2 \phantom{+x_3}  &\leq 13 \notag\\
		x_1,x_2,x_3 &\geq 0, x_1,x_2,x_3 \in \Z \notag
		\end{align*}
        \ee
