Operations research
This or that
Duality pairs students mix up
Do you know the difference? Four duality pairs, answer before me.
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Lesson notes
Write the dual of an LP and interpret shadow prices as value of an extra resource unit
Key points
- Primal max / Dual min: A maximisation primal with ≤ constraints gives a minimisation dual with ≥ constraints.
- Constraint / Dual variable: Each primal constraint becomes one dual variable, and each primal variable becomes one dual constraint.
- Shadow price / Profit per unit: Shadow price is the objective gain per extra resource unit, not a product's unit profit.
- Within range / Unlimited: A shadow price holds only within the range of feasibility, never for unlimited increases.
Takeaway: Shadow prices value extra resources only within the feasibility range.
Quick check: A machine-hour constraint has slack at the optimum. What is its shadow price?
- Equal to unit profit
- Zero
- Negative infinity
An unused resource adds nothing at the margin, so its shadow price is zero.
dual problemshadow pricesensitivity analysis
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