*************** Problem 1 *************** Phase 1: Input dictionary. X3 = -3.00+ 1.00 X1 + 1.00 X2 X4 = 2.00- 3.00 X1 + 4.00 X2 ----------------------------------------------- z = -0.00+ 1.00 X1 + 1.00 X2 Phase 1: Before pivoting to make feasible. X3 = -3.00+ 1.00 X1 + 1.00 X2 + 1.00 X5 X4 = 2.00- 3.00 X1 + 4.00 X2 + 1.00 X5 ----------------------------------------------- z = -0.00+ 0.00 X1 + 0.00 X2 - 1.00 X5 X5 enters. X3 leaves. z = -0.000000 The initial dictionary: X5 = 3.00- 1.00 X1 - 1.00 X2 + 1.00 X3 X4 = 5.00- 4.00 X1 + 3.00 X2 + 1.00 X3 ----------------------------------------------- z = -3.00+ 1.00 X1 + 1.00 X2 - 1.00 X3 X1 enters. X4 leaves. z = -3.000000 After 1 pivot: X5 = 1.75- 1.75 X2 + 0.75 X3 + 0.25 X4 X1 = 1.25+ 0.75 X2 + 0.25 X3 - 0.25 X4 ----------------------------------------------- z = -1.75+ 1.75 X2 - 0.75 X3 - 0.25 X4 X2 enters. X5 leaves. z = -1.750000 After 2 pivots: X2 = 1.00+ 0.43 X3 + 0.14 X4 - 0.57 X5 X1 = 2.00+ 0.57 X3 - 0.14 X4 - 0.43 X5 ----------------------------------------------- z = -0.00+ 0.00 X3 + 0.00 X4 - 1.00 X5 The optimal solution: -0.000000 X1 = 2.0000 X2 = 1.0000 X3 = 0.0000 X4 = 0.0000 The initial dictionary: X2 = 1.00+ 0.43 X3 + 0.14 X4 X1 = 2.00+ 0.57 X3 - 0.14 X4 ----------------------------------------------- z = 3.00+ 1.00 X3 + 0.00 X4 The problem is UNBOUNDED.