Operations research
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3 duality mistakes that quietly cost you marks
Can you name 3 mistakes that cost marks in LP duality?
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Lesson notes
Key points
- Flipping signs wrongly: Students forget a max primal with ≤ constraints gives a min dual with ≥; flip both together.
- Transposing coefficients: Dual constraints come from primal columns, not rows; transpose the coefficient matrix before writing them.
- Misreading shadow prices: A shadow price only holds within the allowable range; beyond it, re-solve before quoting the value.
Takeaway: Max ≤ becomes min ≥, columns become rows, ranges limit prices.
Quick check: A max primal has ≤ constraints; what type are its dual constraints?
- ≥ constraints, min dual
- ≤ constraints, min dual
- = constraints, max dual
Max with ≤ maps to min with ≥ constraints and non-negative dual variables.
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