Two-phase simplex algorithm
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1. Consider the following linear program.
Minimize z = -7x1 + 3x2
subject to 2x1 + 4x2 = 15 (C1)
- 2x1 + x2 ≥ 4 (C2)
Solve the problem using the two-phase Simplex algorithm as follows.
1) (5%) Write the problem in the equality form
2) (5%) Introduce artificial variables, write the objective of Phase I
3) (10%) Set up the Simplex tableau and solve the Phase I problem using steepest ascent rule.
4) (10%) Setup the Simplex tableau in Phase II (10). Notice that you do not have to solve it!
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Solution Summary
This provides an example of working with a linear program and the two-phase Simplex algorithm.
Solution Preview
30%) Consider the following linear program.
Minimize z = -7x1 + 3x2
subject to 2x1 + 4x2 = 15 (C1)
- 2x1 + x2 ≥ 4 (C2)
Solve the problem using the two-phase Simplex algorithm as follows.
1) (5%) Write the problem in the equality form
The original problem is equivalent to
Minimize z = -7x1 + 3x2
subject to 2x1 + 4x2 =15 (C1)
2x1- x2 ≤ -4 (C2)
Therefore in equality form,
Minimize z ...
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