Consider the following LP model:

Maximize z $=4$x$1+14$x$2$

subject to

$2$x$1+7$x$2+$ x$3=21$

$7$x$1+2$x$2+$ x$4=21$

x$1,$ x$2,$ x$3,$ x$40$

Check the optimality and feasibility of each of the following basic solutions: