Consider the following directed network: a. [10 points] Use Dijkstra's algorithm to find shortest paths from node A to each of the nodes B, C, D, and E in the above network by hand (no TORA allowed!). I'm looking for the length of each shortest path, as well as a path itself. Also, list the order in which nodes are added to the set S during the running of Dijkstra's Algorithm. b. [6 points] Write out a linear or (binary) integer programming problem (complete with well-defined decision variables, problem constraints, and nonnegativity constraints) that can be used to find a shortest path from node A to node C. Just write out the problem; do not solve it