Think of complementary slackness as: dual variable × leftover in its matching primal constraint = 0. So if a dual variable is strictly positive (not zero), the only way the product can be zero is if the leftover is zero too — meaning that primal constraint is binding, used up exactly with nothing left over. So the trick is just to scan your dual solution: every strictly positive dual variable points straight at its matching primal constraint and tells you that one must be tight. Where a dual variable is zero, the constraint could be binding or not — complementary slackness gives you no information there.

Complementary slackness dictates that if a dual variable is strictly positive, its corresponding primal slack variable must be zero, meaning the primal constraint must be binding.

When a dual variable is strictly positive, complementary slackness dictates that its corresponding primal constraint must be binding with zero slack.

If a dual variable is strictly positive, complementary slackness tells us that the corresponding primal constraint must be binding. This means the constraint has no unused resources, so its slack is zero. Therefore, a positive dual variable directly indicates which primal constraint must be fully used at the optimal solution.

If a dual variable is strictly positive, its matching primal constraint must be binding (meaning it has zero slack).

If a dual variable is positive, the matching primal constraint must be binding, so its slack is zero.

When a dual variable is strictly positive, the complementary slackness condition requires the corresponding primal slack variable to be zero, meaning the associated primal constraint must hold as an equality and be binding.

By complementary slackness, if a dual variable is strictly positive, its corresponding primal constraint must be binding, meaning its slack = 0.

because a binding constraint can have a zero shadow price, particularly in degenerate or redundant cases.

Complementary slackness establishes a strict mathematical pairing between each primal constraint and its corresponding dual variable. When a dual variable is strictly positive, the mathematical product of that dual variable and its primal slack variable must equal zero. Because the dual variable is non-zero, the corresponding primal slack variable must be driven to exactly zero, which directly forces the associated primal constraint to hold as an equality and be strictly binding.

Complementary slackness dictates that the product of each dual variable and its corresponding primal slack is zero, meaning both cannot be simultaneously non-zero. Therefore, if a dual variable is strictly positive, its associated primal slack must equal zero, forcing that specific primal constraint to hold as an exact equality.

By complementary slackness, if a dual variable is strictly positive, the corresponding primal constraint must be binding. This means its slack is zero because the resource or constraint is fully used at the optimal solution.

By the complementary slackness conditions, the product of a primal constraint's slack variable (si) and its corresponding dual variable (yi) must equal zero at optimality. Consequently, if a dual variable is strictly positive, its corresponding primal slack variable must be zero. A slack of zero means the resource is fully consumed, which guarantees that the associated primal constraint is holding with equality and is therefore binding.

You can interpret complementary slackness by remembering that if a dual variable is strictly positive, the corresponding primal constraint must be binding, meaning its slack is zero. In simple terms, a positive dual variable tells me that the related primal constraint is fully used or active.

By complementary slackness, if a dual variable is strictly positive, the corresponding primal constraint must be binding. In other words, the primal constraint must hold as an equality at the optimal solution.