Visual Proof: Duality in Linear Programming

Discovering the profound symmetry between primal and dual problems in linear programming through visual intuition.

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The Formal Theorem

max profit = min cost

Analytical Intuition.

Duality is the Symmetry of Value. Every optimization problem has a hidden twin. Maximize profit from items is equivalent to minimizing the cost of resources. Shadow Prices tell you the value of one more unit of resource.
CAUTION

Institutional Warning.

The gap between them is the Duality Gap. In linear programming, it is zero?perfect symmetry.

Academic Inquiries.

01

What is a Shadow Price?

The derivative of the optimal value with respect to a constraint bound.

Standardized References.

  • Definitive Institutional SourceInstitutional Reference (nicefa v1)

Institutional Citation

Reference this proof in your academic research or publications.

NICEFA Visual Mathematics. (2026). Visual Proof: Duality in Linear Programming: Visual Proof & Intuition. Retrieved from https://nicefa.org/library/operations-research/linear-programming-duality-visual-proof

Dominate the Logic.

"Abstract theory is just a movement we haven't seen yet."