a) Briefly explain the key fundamental theory used when developing PERT analysis (2 marks) b) State two types of Engineering Projects that you would recommend CPM/PERT method for evaluation the project (2 marks) c) A Manager of the Design and Development Department of City West Water has done a Project Schedule to commence one of their new projects in Melbourne West. The list of activities, their predecessors, and the durations in days are given in the following Table. Please note that the probability tables are attached at the end of this Test paper ID Duration (Time/Days) Predecessor Optimistic (a) Most Likely (m) Pessimistic (b) ABCDEFG None 4 6 14 A 6 11 22 B 3 3. 9 A,C 11 13 27 D 9 12 21 D 6 8 10 E, F 3 5 13 (i) Construct an Activity on Arrow (AOA) Network diagram and determine the expected completion time for the research project, identify the critical activities and the critical path (5 marks) (ii) What would be your estimated time of completion of this project if it has a probability of 99% and the Probability of completing this new project in 70 days? (3 marks)