For the following linear programming problem, the pivot variable is chosen to be the one with the largest positive coefficient in the z row. After 6 pivots, the dictionary is the same as the one we started with. This results in an infinite loop.
Input file: 4 3 10 -57 -9 -24 0 0.5 -5.5 -2.5 9 0 0.5 -1.5 -0.5 1 1 1 0 0 0 *************** Problem 1 *************** Phase 1: Input dictionary. X5 = 0.00- 0.50 X1 + 5.50 X2 + 2.50 X3 - 9.00 X4 X6 = 0.00- 0.50 X1 + 1.50 X2 + 0.50 X3 - 1.00 X4 X7 = 1.00- 1.00 X1 + 0.00 X2 + 0.00 X3 + 0.00 X4 ----------------------------------------------- z = -0.00+ 10.00 X1 - 57.00 X2 - 9.00 X3 - 24.00 X4 The initial dictionary: X5 = 0.00- 0.50 X1 + 5.50 X2 + 2.50 X3 - 9.00 X4 X6 = 0.00- 0.50 X1 + 1.50 X2 + 0.50 X3 - 1.00 X4 X7 = 1.00- 1.00 X1 + 0.00 X2 + 0.00 X3 + 0.00 X4 ----------------------------------------------- z = -0.00+ 10.00 X1 - 57.00 X2 - 9.00 X3 - 24.00 X4 X1 enters. X5 leaves. z = -0.000000 After 1 pivot: X1 = 0.00+ 11.00 X2 + 5.00 X3 - 18.00 X4 - 2.00 X5 X6 = 0.00- 4.00 X2 - 2.00 X3 + 8.00 X4 + 1.00 X5 X7 = 1.00- 11.00 X2 - 5.00 X3 + 18.00 X4 + 2.00 X5 ----------------------------------------------- z = -0.00+ 53.00 X2 + 41.00 X3 - 204.00 X4 - 20.00 X5 X2 enters. X6 leaves. z = -0.000000 After 2 pivots: X1 = 0.00- 0.50 X3 + 4.00 X4 + 0.75 X5 - 2.75 X6 X2 = 0.00- 0.50 X3 + 2.00 X4 + 0.25 X5 - 0.25 X6 X7 = 1.00+ 0.50 X3 - 4.00 X4 - 0.75 X5 + 2.75 X6 ----------------------------------------------- z = -0.00+ 14.50 X3 - 98.00 X4 - 6.75 X5 - 13.25 X6 X3 enters. X1 leaves. z = -0.000000 After 3 pivots: X3 = 0.00- 2.00 X1 + 8.00 X4 + 1.50 X5 - 5.50 X6 X2 = 0.00+ 1.00 X1 - 2.00 X4 - 0.50 X5 + 2.50 X6 X7 = 1.00- 1.00 X1 + 0.00 X4 + 0.00 X5 + 0.00 X6 ----------------------------------------------- z = -0.00- 29.00 X1 + 18.00 X4 + 15.00 X5 - 93.00 X6 X4 enters. X2 leaves. z = -0.000000 After 4 pivots: X3 = 0.00+ 2.00 X1 - 4.00 X2 - 0.50 X5 + 4.50 X6 X4 = 0.00+ 0.50 X1 - 0.50 X2 - 0.25 X5 + 1.25 X6 X7 = 1.00- 1.00 X1 + 0.00 X2 + 0.00 X5 + 0.00 X6 ----------------------------------------------- z = -0.00- 20.00 X1 - 9.00 X2 + 10.50 X5 - 70.50 X6 X5 enters. X3 leaves. z = -0.000000 After 5 pivots: X5 = 0.00+ 4.00 X1 - 8.00 X2 - 2.00 X3 + 9.00 X6 X4 = 0.00- 0.50 X1 + 1.50 X2 + 0.50 X3 - 1.00 X6 X7 = 1.00- 1.00 X1 + 0.00 X2 + 0.00 X3 + 0.00 X6 ----------------------------------------------- z = -0.00+ 22.00 X1 - 93.00 X2 - 21.00 X3 + 24.00 X6 X6 enters. X4 leaves. z = -0.000000 After 6 pivots: X5 = 0.00- 0.50 X1 + 5.50 X2 + 2.50 X3 - 9.00 X4 X6 = 0.00- 0.50 X1 + 1.50 X2 + 0.50 X3 - 1.00 X4 X7 = 1.00- 1.00 X1 + 0.00 X2 + 0.00 X3 + 0.00 X4 ----------------------------------------------- z = -0.00+ 10.00 X1 - 57.00 X2 - 9.00 X3 - 24.00 X4