True or False (a) Given a linear program in canonical form, if we pivot using the simplex rule, then a strict decrease in the objective function value is obtained. (b) If the feasible region for a linear program is unbounded, then no finite optimal value exists. (c) If a linear program is in canonical form, then a pivot by the successive ratio rule yields a tableau with each constraint row being lexicographically positive. (d) A linear program in canonical form always has a feasible solution. (e) If A is a 3 x 6 matrix, a linear program with the feasible set {x | Ax = b, x 2 0} may have 125 basic feasible solutions. (f) The tableau below for a linear program in standard form shows that the linear program has no finite minimum value. -2 1 0 - 1 -1 -2 0 1 0 1 0 1 0 1 1 (8) Every tableau in standard form can be put into canonical form by an appropriate sequence of pivots. (h) If a linear program is feasible and if an artificial variable remains as a basic variable after the artificial problem has been solved, then the corresponding con- stant column entry could be positive. (i) If a tableau is in canonical form and if the cost coefficient of a nonbasic variable is negative, then the associated basic feasible solution could not be optimal