The Weak Duality Theorem: Linear Programming Intuition

A common misconception is to equate Weak Duality with Strong Duality, assuming \

c^T x = b^T y \

for any feasible \

x \

and \

y \

. Weak Duality only guarantees the inequality; equality (and thus optimality) requires additional conditions, which is the domain of Strong Duality.

Institutional Reference: Linear and Integer Programming