Exercise 3.18 Consider the simplex method applied to a standard form problem and assume that the rows of the matrix A are linearly independent. For each of the statements that follow, give either a proof or a counterexample. (a) An iteration of the simplex method may move the feasible solution by a positive distance while leaving the cost unchanged. (b) A variable that has just left the basis cannot reenter in the very next iteration. (c) A variable that has just entered the basis cannot leave in the very next iteration. (d) If there is a nondegenerate optimal basis, then there exists a unique optimal basis. (e) If x is an optimal solution, no more than m of its components can be positive, where m is the number of equality constraints