$(10$ pts$)$ This question is concerned with the following linear program:

Minimize $12x_1+x_2+21x_3-x_4-7x_5,$

Subject $to-x_1-4x_2-2x_3+x_4+x_5=5$

$3x_1+x_2,-2x_4+5x_5=14$

$x_1-7x_2+6x_3+3x_4-2x_5=7$

$x_1,$dots,$x_{5}0$

Suppose that $x_3,x_4,x_5$ are currently the basic variables. Use the matrix form of Simplex

method below.

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

the leaving variable?