*************** 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
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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