Consider the following statements about linear programming and the simplex method. Label each statement as True or False and then justify your answer.

a$.$ The simplex method's minimum ratio rule for choosing the leaving basic variable is used because making another choice with a larger ratio would yield a basic solution that is not feasible.

b$.$ In a particular iteration of the simplex method, if there is a tie for which variable should be the leaving basic variable, then the next basic feasible solution must have at least one basic variable equal to zero.

c$.$ If there is no leaving basic variable at a particular iteration, then the problem has no feasible solutions.

d$.$ If at least one of the basic variables has a coefficient of zero in the $z-$row of the final tableau, then the problem has multiple optimal solutions.