Consider the $LP$ problem:

MIN $z=2x_1-3x_2+x_3+x_4$

$s.t.x_1-2x_2-3x_3-2x_4=3$

$x_1-x_2+2x_3+x_4=11$

$x_1,x_2,x_3,x_{4}0$

After phase and phase $2,$

$we$ arrime $at$ the following

optumal tablean:

$([x_1,x_2,x_3,x_4,19],[1,0,7,4,19],[0,1,5,3,8],[0,0,2,2,z-14])$

$(a)$ What $b$ the optanal solution

$to$ Thes problem?

$(b)$ Suppose the objecthe

function $is$ changed $to$

MINz$=3x_1-3x_2+x_3+x_4$

Will the opthmal soluteon

found $in(a)$ Still $be$ optimal?

$If$ not, find the rew optinal solution without

resolving' the problem from the beginnung

$Cl.$ use $sensitivityandysison$ the previous optableaue.