For any linear programming problem in our standard form and its dual problem, label each of the following statements as true or false and then justify your answer.

(a) The sum of the number of functional constraints and the number of variables (before augmenting) is the same for both the primal and the dual problems.

(b) At each iteration, the simplex method simultaneously identifies a CPF solution for the primal problem and a CPF solution for the dual problem such that their objective function values are the same.

(c) If the primal problem has an unbounded objective function, then the optimal value of the objective function for the dual problem must be zero.