c$.$ Consider the following LP

Maximize $z=5x_1+2x_2+3x_3$

Subject to

$x_1+5x_2+2x_3=15$

$x_1-5x_2-6x_{3}20$

$x_1,x_{2}0$

Given that the artificial variable $x_4$ and the slack variable $x_5$ form the starting basic variables and that $M$ was set equal to $100$ when solving the problem. the optimal tableau is given as:

$\backslash$table$[[$Basic$,x_1,x_2,x_3,x_4,x_5,$Solution$],[z,0,23,7,105,0,75],[x_1,1,5,2,1,0,15],[x_5,0,-10,-8,-1,1,5]]$

Write the associated dual problem, and determine its optimal solution in two ways