Label each of the following statements about linear programming problems as true or false, and then justify your answer.

(a) If a feasible solution is optimal but not a CPF solution, then infinitely many optimal solutions exist.

(b) If the value of the objective function is equal at two different feasible points x^* and x^**, then all points on the line segment connecting x^* and x^** are feasible and Z has the same value at all those points.

(c) If the problem has n variables (before augmenting), then the simultaneous solution of any set of n constraint boundary equations is a CPF solution.