Consider the following problem:

Maximize z = 3x1 + 2x2 + 3x3 subject to 2x1 + x2 + x3 = 4 x1 + 3x2 + x3 = 12 3x1 + 4x2 + 2x3 = 16 x1, x2, x3 Ú 0

(a) Show that Phase I terminates with two zero artificial variables in the basic solution

(use TORA for convenience).

(b) Show that when the procedure of Problem 3-47

(b) is applied at the end of Phase I, only one of the two zero artificial variables can be made nonbasic.

(c) Show that the original constraint associated with the zero artificial variable that cannot be made nonbasic in

(b) must be redundant—hence, its row and its column can be removed at the start of Phase II.