1. Let F be the face of optimal solutions of the linear program max P x R : Ax b . n Let M F cx : x P , where be the equality set of F and let u* be any optimal solution of the dual linear program. Show that ui* 0 if i M F 2. Consider the polyhedron P described by x1 x2 0 x1 x 2 1 2 x2 5 8x1 x 2 16 x1 x 2 4 x R2 For each face F of P in Above problem, find the values of c such that max the set of optimal solutions. cx : x P has F as