Consider the following linear programming $($LP$)$ problem.

Maximize $Z=-5x_1+5x_2+13x_3$

subject to:

$-1x_1+1x_2+3x_{3}20$

$12x_1+4x_2+10x_{3}90$

$x_{1}0,x_{2}0,x_{3}0.$

a$.$ Construct the augmented form of this LP by introducing slack variables. $(10$ pts$)$

b$.$ The final simplex tableau for the above LP is given below.

$\backslash$table$[[\backslash$table$[[$Basic$],[$Variable$]],Eq,$Coefficient of:$,\backslash$table$[[$Right$],[$Side$]]],[Z,x_1,x_2,x_3,x_4,x_{5\text{S}\text{o}\text{l}\text{v}\text{e}it\text{c}\text{o}\text{r}\text{r}\text{e}\text{c}\text{t}\text{l}\text{y}\text{p}\text{l}\text{e}\text{a}\text{s}\text{e}}$