True or False.

$($i$)$ If the problem has a nondegenerate optimal solution, then it has a unique optimal

solution.

$($ii$)$ If the feasible set is unbounded then the problem is unbounded.

$($iii$)$ If you correctly apply the Simplex Method to a feasible dictionary then the new

dictionary is feasible.

$($iv$)$ If the problem has a unique optimal solution, then this solution is nondegenerate.

$($v$)$ If any $b_i$ is negative then the problem is automatically infeasible.

$($vi$)$ If this problem is bounded then the feasible set is bounded.