We want to apply the critical path method (cpm) to the following set of 7 project activities a, b..., 8. The duration time dependencies of the activities are denoted in the following table, e.g. you have to finish first a before you can start activitiy d. It may be helpful to examine the solution of exercise 3, sheet 3. activity duration depends on A 1 B 3 A 2 B D 4 A E 3 F 4 CE G 3 CD WWNW a) For each activity X determine earliest starting time I (x). You should use the topological ordering A, B, C, D, E, F, G (the dependency graph is acyclic). Transform the problem to a suitable Digraph with 16 nodes, for each activity X a start node vx and an end node wx together with an additional source s and a target node t. The edge costs are negative. Solve a shortest path problem to obtain a longest path in the original graph. b) Assume, the activities in the critical path are performed without delay, so the total time equals the length of this path. Determine for each activity X the latest end time T (X). To do this, reverse the ordering, the role of s and t and also the topological ordering. Then compute a shortest distance form start node t. c) Assume, it is possible to solve the jobs in parallel. Find a schedule using a minimal number of machines