( 2 points each, total 40 points) For each one of the following statements, state whether it is true or false. If true, provide a proof, else, provide a counterexample. For each one of the questions, provide a brief answer and explanation. (a) If a simplex pivot does not result in an improvement of the objective function, then both basic solutions (before and after the pivot) must be degenerate. (b) If we pivot at a degenerate BFS, the minimum ratio must be zero. (c) In a simplex tableau, if there is a tie in minimal ratio test, then the basic feasible solution after the pivot must be degenerate