This question is concerned with the following linear program:

Suppose that x$3,$ x$4,$ x$5$ are currently the basic variables. Use the matrix form of Simplex

method below.

Minimize $12$x$1+$x$2+21$x$3-$x$4-7$x$5$

subject to $-$x$1-4$x$2-2$x$3+$x$4+$x$5=5$

$3$x$1+$ x$2-2$x$4+5$x$5=14$

x$1-7$x$2+6$x$3+3$x$4-2$x$5=7$

x$1,.....$x$5>0$

a$).$ What is the current basic solution x$=($x$1,$x$2$ x$3,$ x$4,$ x$5)?$

b$).$ What non$-$basic variables are candidates to enter the basis?

c$).$ If x$2$ is chosen to enter the basis, what happens when you try to determine