13. Consider the following statements and state, in each case, whether it is true or false. In case the statement is false, state the correct position:

(i) The addition of a new constraint in a linear programming problem can improve the value of the objective function.

(ii) In the simplex method, any variable which is removed from the basis at an iteration cannot re-enter the basis at the next iteration.

(iii) If, in the final simplex tableau of a linear programming problem, any basic variable has a value of zero in the quantity column, the problem has multiple optimal solutions.

(iv) If an optimal solution is degenerate, it is meaningless to the manager.