Operations research
Top 3
3 LP Special Cases Examiners Love
Three LP special cases will be on your exam. Wait for number one.
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Lesson notes
Key points
- 3. Unbounded solution: The feasible region is open in the improving direction, so profit grows forever, usually a missing constraint.
- 2. Infeasible problem: Constraints contradict each other, so no point satisfies them all and no feasible region exists.
- 1. Multiple optima: When the objective line is parallel to a binding constraint, every point on that edge is optimal.
Takeaway: Check for unbounded, infeasible and multiple optima every time.
Quick check: What causes an LP to have infinitely many optimal solutions?
- Objective parallel to edge
- Contradictory constraints
- A missing upper bound
A parallel objective touches a whole edge, so every point there ties.
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