Use the BIP branch$-$and$-$bound algorithm presented in Sec. $12\mathrm{.}6$ to solve the following problem interactively:

Minimize Z $=5$x $+6$x $+7$x $+8$x $+9$x $,$

subject to

$3$x $$ x $+$ x $+$ x $2$x $>=2$

x$1+3$x$2$ x$32$x$4+$ x$5>=0$

$$x$1$ x$2+3$x$3+$ x$4+$ x$5>=1$

and

xj is binary, for j $=1,2,...,5.$