A constraint is binding if it left hand side of a constraint is equal to the right hand side after the optimal solution is plugged into the constraint function.

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This true/false item asks whether a constraint is binding when, at the optimal solution, its left-hand side equals the right-hand side after substituting the solution.
Option 1: True. In linear programming and optimization, a constraint is binding (or tight) at the optimum if the value of the left-hand side equals the right-hand side when you plug in the optimal solution. This means the constraint is active and the corresponding slack is zero, indicating no room to improve the objective without violating that constraint.
Option 2: False. If a constraint were not binding (nonbinding), the left-hand side would be strictly less than (or greater than, depending on the inequality direction) the right-hand side, yielding a positive slack. In that case, the constraint does not touch the feasible region's boundary at the optimum, which contradicts the definition of binding.
Option 1 aligns with the formal concept of binding constraints, where the constraint is active and the solution lies exactly on its boundary. Option 2 contradicts this by describing a nonbinding, slack-filled situation that does not hold for a binding constraint.
In summary, the statement describes the standard criterion for binding constraints: equality at the optimum and zero slack, which is the hallmark of an active constraint.

BU.520.601.T2.FA25 Final Exam

A constraint is binding if it left hand side of a constraint is equal to the right hand side after the optimal solution is plugged into the constraint function.

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