$(3).$ A minimization LP is being solved by the BigM Method. $s_2,s_3$ are the slack variables in constraints

$2,3,e$ is the excess variable for the first constraint, and $a_1$ is the artificial variable of constraint $1.$ The tableau

below is optimal:

Which one of the following statements is true. Explain briefly.

$($i$).$ The original LP is not feasible.

$($ii$).$ The original LP is feasible but does not have a BFS$.$

$($iii$).$ The tableau shows a BFS for the original LP which is optimal.

$($iv$).$ The tableau shows a BFS for the original LP which is not optimal.