Exercise: Consider a linear programming problem in a standard form and assume that the rows of A matrix are linearly independent. For each one of the following statements, provide either a proof or a counterexample. (a) Let x* be a basic feasible solution. Suppose that for every basis corresponding to x*, the associated basic solution to the dual is infeasible. Then, the optimal cost must be strictly less that c'x*. (b) The dual of the auxiliary primal problem considered in Phase I of the simplex method is always feasible. (c) Let pi be the dual variable associated with the ith equality constraint in the primal. Eliminating the ith primal equality constraint is equivalent to introducing the additional constraint Pi = 0 in the dual problem. (d) If the unboundedness criterion in the primal simplex algorithm is satisfied, then the dual problem is infeasible