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:

$($a$)$ Basic variables $=1$x$2,$ x$42,$ Inverse $=$ a

$1$

$70$

$-2$

$71$b

$($b$)$ Basic variables $=1$x$2,$ x$32,$ Inverse $=$ a

$01$

$2$

$1-7$

$2$

b

$($c$)$ Basic variables $=1$x$2,$ x$12,$ Inverse $=$ a

$7$

$45-2$

$45$

$-2$

$45$

$7$

$45$

b

$($d$)$ Basic variables $=1$x$1,$ x$42,$ Inverse $=$ a

$1$

$20$

$-7$

$21$b