A binding constraint passes directly through the optimal solution point on the final graph, actively restricting the feasible region so that its slack or surplus is zero. Relaxing or shifting a binding constraint pushes the optimal point and directly changes the objective value.

A non-binding constraint sits away from the optimal solution point, leaving a non-zero slack or surplus margin. Because it does not touch or limit the optimal point on the final graph, small changes to its limit do not affect the current optimal solution or objective value.

A binding constraint is a constraint that the optimal solution reaches exactly, meaning there is no unused resource or slack. On the final graph, the optimal point lies directly on that constraint line. A non-binding constraint is one that has some unused capacity, so the optimal solution does not lie on its line and there is slack remaining. In simple terms, binding = fully used resource, while non-binding = resource still has some available capacity.

Binding constraint: it touches the best point — used up fully, no slack left. If you shift it, your answer changes.

Non-binding constraint: it sits away from the best point — has leftover space, slack. Shifting it a bit does nothing to your answer.

On the graph: binding forms the edge/corner where the solution sits; non-binding is just a line that doesn’t touch that spot at all.