please explain why each is true or false

5.1-10. Label each of the following statements about linear pro- gramming 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 equa- tions is a CPF solution