We can write the transshipment problem from the last couple of lectures as the problem of minimize cx s.t. Ax = -b, x20 If we view this as a primal problem, then its dual is maximize - by s.t. Ay +z = c, z 20 I will note that when we select a root node in the primal, you can choose to view this as the corresponding y being fixed at 0. 1. If you use the example we've been working on in class, what should the dimensions of y and z be in order for the above dual to make sense (for instance, in terms of ensuring the matrix-vector multiplication is possible)? Can you interpret the dual variables y and z in terms of the network problem? 2. Complementary slackness in previous chapters meant, in part, that at the optimal solution x, we had that the dual solution resulted in slack variables which had entries which were 0 whenever the corresponding entries of this optimal x were nonzero. Can you identify what this condition would mean in terms of the network? 3. Looking at the iteration we performed previously, identify the dual variables (including the slack) corresponding to the initial primal spanning tree solution. Was this initial dual feasible? What happened to the dual when we performed a pivot on the primal problem (selecting an entering arc and leaving arc)