(Duality for Nonnegativity Constraints) Consider the version of the minimum cost flow problem where there are nonnegativity constraints which supports from below the set S, and is normal to the vector...

(Duality for Nonnegativity Constraints) Consider the version of the minimum cost flow problem where there are nonnegativity constraints

which supports from below the set S, and is normal to the vector (−p, 1). The dual problem is to find a price vector p for which the intersection point is as high as possible. The figure illustrates the equality of the lowest common point of S and L (optimal primal cost), and the highest point of intersection of L by a hyperplane that supports S from below (optimal dual cost).