Consider the following IP problem:

min Z $=2$x$1+3$x$2$

s$.$t$.$ x$1+$ x$2>=3$

x$1+3$x$2>=6$

x$1,$ x$2>=0$

x$1,$ x$2$ are integers

$($a$)$ Use the MIP branch$-$and$-$bound algorithm to solve this problem by hand. For each

subproblem, solve its LP relaxation