$(20$ pts$)$ You are using the matrix form of Simplex method to solve the following linear

programming problem.

Maximize $,Z=6x_1+5x_2-x_3+4x_4,$

subject to

$3x_1+2x_2-3x_3+x_{4}120$

$3x_1+3x_2+x_3+3x_{4}180$

and

$x_{1}0,x_{2}0,x_{3}0,x_{4}0.$

You have obtained the following final simplex tableau where $x_5$ and $x_6$ are the slack

variables for the respective constraints.

Use the fundamental insight presented in class and also in the textbook to identify $Z^{**},b_1^{**},$ and

$b_2^{**}.$