answer the whole full question

4. Consider a LP model with bounded feasible region. Label each of the follow- ing statements about linear programming problems as true or false, and then justify your answer. (1) If a feasible solution is optimal but not a CPF solution, then infinitely many optimal solutions exist. (2) 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 fea- sible and Z has the same value at all those points. (3) If the problem has n variables (before augmenting), then the simultaneous solution of any set of n constraint boundary equations is a CPF solution