*************** Problem 1 *************** Maximize 28.00 X1 +11.00 X2 subject to 14.00 X1 + 6.00 X2 <= 25.00 X1 , X2 >= 0 Phase 1: Input dictionary. X3 = 25.00 -14.00 X1 - 6.00 X2 ------------------------------------------------- z = -0.00 +28.00 X1 +11.00 X2 The final dictionary: X1 = 1.79 - 0.43 X2 - 0.07 X3 ------------------------------------------------- z = 50.00 - 1.00 X2 - 2.00 X3 The optimal solution: 50.00 X1 = 1.79 X2 = 0.00 X3 = 0.00
Notes 7.2, Page 2
*************** Problem 2 *************** Maximize 28.00 X1 +11.00 X2 subject to 14.00 X1 + 6.00 X2 <= 25.00 1.00 X1 + 0.00 X2 <= 1.00 X1 , X2 >= 0 Phase 1: Input dictionary. X3 = 25.00 -14.00 X1 - 6.00 X2 X4 = 1.00 - 1.00 X1 + 0.00 X2 ------------------------------------------------- z = -0.00 +28.00 X1 +11.00 X2 The final dictionary: X2 = 1.83 - 0.17 X3 + 2.33 X4 X1 = 1.00 + 0.00 X3 - 1.00 X4 ------------------------------------------------- z = 48.17 - 1.83 X3 - 2.33 X4 The optimal solution: 48.17 X1 = 1.00 X2 = 1.83 X3 = 0.00 X4 = 0.00
Notes 7.2, Page 3
*************** Problem 3 *************** Maximize 28.00 X1 +11.00 X2 subject to 14.00 X1 + 6.00 X2 <= 25.00 1.00 X1 + 0.00 X2 <= 1.00 3.00 X1 + 1.00 X2 <= 4.00 X1 , X2 >= 0 Phase 1: Input dictionary. X3 = 25.00 -14.00 X1 - 6.00 X2 X4 = 1.00 - 1.00 X1 + 0.00 X2 X5 = 4.00 - 3.00 X1 - 1.00 X2 ------------------------------------------------- z = -0.00 +28.00 X1 +11.00 X2 The final dictionary: X3 = 1.00 + 4.00 X1 + 6.00 X5 X4 = 1.00 - 1.00 X1 + 0.00 X5 X2 = 4.00 - 3.00 X1 - 1.00 X5 ------------------------------------------------- z = 44.00 - 5.00 X1 -11.00 X5 The optimal solution: 44.00 X1 = 0.00 X2 = 4.00 X3 = 1.00 X4 = 1.00 X5 = 0.00