1) Determine whether the below statements are correct or not. [32] a) When an artificial problem is created by introducing artificial variables and using the Big M method, if all artificial variables in current solution for the artificial problem are equal to zero, then the current solution is an infeasible solution in the real (original) problem. b) The simplex methods rule for choosing the entering basic variable always leads to the best adjacent BF solution (Largest Z value). c) In a particular iteration of the simplex method, if there is a tie for which variable should be the leaving basic variable, then the next basic feasible solution must have at least one basic variable equal to zero. d) To choose the new CPF solution to move to from the current CPF solution, the simplex method identifies all the adjacent CPF solutions and determines which one gives the largest rate of improvement in the value of the objective function. e) Given that a standard form (maximization and all constraints inequalities are less than and equal to) LP formulation with 3 decision variables and 4 functional constraints, there are 4 basic variables and 3 non-basic variables. f) Assume that the feasible region exists and is bounded. If multiple optimal solutions exist, then an optimal CPF solution may have an adjacent CPF solution that also is optimal (the same value of Z). g) Only CPF solutions can be optimal, so the number of optimal solutions cannot exceed the number of CPF solutions. h) If the initial tableau is: Basic Eq Coefficient of Right Variable No Z x1 x2 x3 x4 Side Z 0 1 1 -1 0 0 0 x3 1 0 2 -1 1 0 20 x4 2 0 1 -2 0 1 20 Then, the problem has no feasible solutions.