$1.$ Consider the following LP problem.

Minimize $=4!+"$ subject to $3!+"=3$

$4!+3">=6!+2"<=4$

$!,">=0$

$($i$)$ Use the Big M method, with $=100,$ to construct the complete first simplex tableau for the simplex method and identify the corresponding initial basic feasible solution. Also identify the initial entering non $$ basic variable and the leaving basic variable.

$($ii$)$ Perform one iteration of the simplex method.