( 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. (d) In the simplex method, if one of the reduced costs is negative, then the current basic feasible solution is not optimal. (e) In a revised simplex tableau, if cjzj