(a) Prove that, in a Pigou like network with affine cost function, an optimal flow f* routes all traffic on paths with cost at most twice that of a shortest path (according to the travel ties induced by f*). (b) Prove that, in a two node, two edge network with affine cost functions, an optimal flow f* routes all traffic on paths with cost at most twice that of a shortest path (according to the travel ties induced by f*)