The solution to a linear programming problem must always lie on a constraint.

Name: The solution to a linear programming problem must always lie on a constraint.
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This is because the feasible region (i.e. the region defined by all the constraints) is where the optimal solution must lie. The feasible region is comprised of the intersection of all the constraint lines/curves/planes, and therefore the solution to the linear programming problem must lie on one of these constraints.

The Solution to a Linear Programming Problem Must Always Lie