Solve the following ILP problem max z $=4$x$1+3$x$2+$ x$3$ s$.$t$.3$x$1+2$x$2+$ xx$1+$ x$2+2$x x$1,$ x$2,$ x$30$; x$1,$ x$2,$ x$3$ integer $($a$)(25$ pts$)$ Use the cutting plane method to solve the ILP problem above. $($b$)(25$ pts$)$ Use the branch$-$and$-$bound method to solve the ILP problem above.$(50$ pts$)$ Solve the following ILP problem

maxz$=4x_1+3x_2+x_3$

$s.t.3x_1+2x_2+x_{3}7$

$2x_1+x_2+2x_{3}11$

$x_1,x_2,x_{3}0$;$x_1,x_2,x_3$ integer

$($a$)(25$ pts$)$ Use the cutting plane method to solve the ILP problem above.

$($b$)(25$ pts$)$ Use the branch$-$and$-$bound method to solve the ILP problem above.