Given the following activities for a project: Activity Duration Immediate Activity Optimistic Most Likely Pessimistic Predecessor B 5 8 6 9 7 9 7 10 8 10 8 D E Jaco con 4 U AUHIM Nuno DO 1 UAH S 8 11 10 14 2 HO 10 9 13 1 D BE E,G,H BE 1,J J 12 11 15 3 (a) Draw an Activity-on-Arrow (AOA) network diagram representing the project. Put the node numbers in circles and draw arrow from node to node, labeling each arrow with the activity letter and duration as PERT weighted average. (b) Identify all of the paths on the network diagram and note how long they are, using Figure 6-8 as a guide for how to represent each path. Be sure to round up the duration for all activities. (c) What is the critical path for this project and how long is it? (d) What is the shortest possible time it will take to complete the project? (e) Draw manually the appropriate network diagram (using PDM) and then find (and also provide as a table) for each of the activities by d: early start (ES), early finish (EF), late start (LS), late finish (LE) and free floats and total slacks and provide them in a table form