Operations research
Guess first
Can a Simplex Pivot Gain Nothing?
Most students get this simplex question wrong. Guess first.
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Lesson notes
Key points
- When a basic variable equals zero, the solution is degenerate, and the ratio test can pick a pivot with zero step size.
- The basis changes but you stay at the same corner, so the objective value does not move, and rarely simplex can cycle.
Definitions
- Degenerate solution
- A basic feasible solution where at least one basic variable equals zero.
Takeaway: Degenerate pivots change the basis without improving the objective.
Quick check: In a maximisation simplex, can a pivot leave the objective value unchanged?
- No, it must rise
- No, it would be infeasible
- Yes, if degenerate
A tie in the ratio test signals degeneracy: a pivot may gain zero.
DegeneracySame corner
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