(a) Consider the problem of finding a shortest path tree rooted at a particular node. Show how this problem can be formulated as an out-of-kilter flow problem. Note that we would almost certainly...

(a) Consider the problem of finding a shortest path tree rooted at a particular node. Show how this problem can be formulated as an out-of-kilter flow problem. Note that we would almost certainly never solve this problem in this way, but it is useful to know how to transform a problem into this format. Illustrate your approach on the network in Figure 2.51 for the shortest path tree rooted at node A.

(b) Formulate the problem of finding the shortest path from node s to all other nodes in a network as an optimization problem. Clearly define all decision variables and all inputs. State the objective function and all constraints in both words and using the notation you have defined.