Operations research
Myth vs fact
Myth: A Zero Basic Variable Means You Made an Error
A basic variable equal to zero? Most students think they broke the simplex.
Quick check · tap an answer to continue
Lesson notes
Key points
- When more constraints than needed pass through one corner, a basic variable can take the value zero; this is called degeneracy.
- A tie in the minimum ratio test is the usual warning sign, so the next pivot may change the basis without improving the objective.
Definitions
- Degenerate solution
- A basic feasible solution where at least one basic variable equals zero.
Myth: A basic variable equal to zero means your simplex tableau is wrong
Fact: A zero basic variable signals degeneracy, a valid corner, not an error
Takeaway: Zero in the basis means degeneracy, not a mistake.
Quick check: Myth or fact: degeneracy can make simplex pivot without improving Z.
- Myth
- Fact
- Depends
At a degenerate corner, a pivot can change the basis while Z stays the same.
DegeneracyRatio tie
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