Operations research
Guess first
Can a Simplex Pivot Make Zero Progress?
Most students get this simplex question wrong
Quick check · tap an answer to continue
Lesson notes
Key points
- When a basic variable equals zero, the solution is degenerate, and a pivot can change the basis without moving the objective at all.
- In rare cases simplex can even cycle through the same bases forever, which is why Bland's rule exists to guarantee it stops.
Definitions
- Degenerate solution
- A basic feasible solution where at least one basic variable equals zero
Quick check: A simplex pivot changes the basis. Must the objective value strictly improve?
- Yes, every time
- Only on the last pivot
- No, it can stay the same
Degenerate pivots change the basis but can leave the objective unchanged.
DegeneracyCycling
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