Operations research
Tier list
Ranking LP Special Cases by Exam Trickiness
Ranking LP special cases by how often they trap you in exams.
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Lesson notes
Key points
- Infeasible problem: No region satisfies all constraints, and artificial variables stay positive in phase one.
- Unbounded solution: No positive ratio in the entering column means the objective can grow forever.
- Multiple optimal solutions: A zero reduced cost for a nonbasic variable at optimum signals alternative optima.
Takeaway: Zero reduced cost on a nonbasic variable means multiple optima.
Quick check: In a final simplex tableau, what signals alternative optimal solutions?
- Nonbasic reduced cost of zero
- Positive artificial variable
- No positive pivot ratio
A zero reduced cost lets a variable enter without changing the objective.
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