Consider the path flow formulation of the multi commodity flow problem of Section 8.8.7. Assume that for each OD pair (im, jm) there is a "reverse" OD pair (jm, im), and let cm > 0 be the ratio of the supplies of these two OD pairs. Suppose that there is the restriction that the paths used by the OD pair (im, jm) must be the reverse of the paths used by the OD pair (jm, im) and the ratios of the corresponding flows must be cm; that is, if hp is the flow carried by a path p from im to jm, then cmhp must be the flow of the reverse path of p, from jm to im. Derive an optimality condition like the one of Prop. 8.5, and the forms of the conditional gradient and gradient projection methods for this problem.