$[$Optimisation$]$ 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 bi is negative then the problem is automatically infeasible.

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

$($vii$)$ If this problem has a $($nonempty$)$ bounded feasible set then the problem is bounded.

$($viii$)$ Say m $=4$ and n $=3.$ Then any basic feasible solution to this problem will have at

least $3$ variables that are equal to $0.$

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

$($x$)$ If each bi $>=0$ then the problem is feasible.

$($xi$)$ Degeneracy always leads to cycling.

$($xii$)$ Cycling can only occur if some basic solution is degenerate.

$($xiii$)$ If the optimal value of the auxiliary problem is $-10$ then the original problem is

infeasible.

$($xiv$)$ A problem with $2$ constraints and $3$ decision variables has at most $20$ basic feasible solutions.