$12\mathrm{.}4\mathrm{.}2.$ Consider the two$-$variable IP example discussed in Sec. $12\mathrm{.}5$

and illustrated in Fig. $12\mathrm{.}2.$

$($a$)$ Use a binary representation of the variables to reformulate this

model as a BIP problem.

FIGURE $12\mathrm{.}2$

An example where rounding

an optimal solution for the LP

relaxation is far from optimal

for the IP problem.