Use the branch$-$and$-$bound method to find the optimal solution to the following LPs

a$.$ max z$=7$x$1+3$x$2$

s$.$t; $2$x$1+$ x$2<=9$

$3$x$1+2$x$2<=13$

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

Worker Time $($hours$)$

Job $1$ Job $2$ Job $3$ Job $4$

$110-1015$

$2128-16$

$31291218$

$46121518$

$516-812$

b$.$ max z$=4$x$1+3$x$2+$ x$3$

s$.$t; $3$x$1+2$x$2+$ x$3<=7$

$2$x$1+$ x$2+2$x$3<=11$

x$1,$x$2,$x$3>=0$ ; x$2,$x$3$ integer