m b Question 1 (60 marks) The following activity data is known. Where a is the optimistic time, m is the most likely time, b is the pessimistic time for the activities. Time (days) Activity Predecessor a 1 2 4 6 2 S 5 5 3 2 3 5 7 4 1 7 10 13 5 1 11 12 13 6 2,4 5 6 7 7 3 9 10 11 8 3,6 5 7 9 9 4 7 9 11 10 5 3 3 3 11 7 15 17 19 12 8 6 8 10 13 9.10 7 8 15 14 7 12 14 16 15 12,13 16 17 18 It is also known that the project network has the following seven paths. 1) 1-4-9-13-15 2) 1-5-10-13-15 3) 1-4-6-8-12-15 4) 2-3-7-11 5) 2-3-7-14 6) 2-3-8-12-15 7) 2-6-8-12-15 Simulate the project duration using Monte Carlo Simulation. Use the Model Risk simulator in Excel or any other suitable software. A. Perform each simulation run with 1000, 5000, and 10000 trials. For each simulation run, report the mean duration, standard deviation, the duration for 80% and 40% probabilities of completion. B. Report the screenshots of percentile values and histograms for each simulation run. C. For 10000-trial simulation, report the probability of the occurrence of each of the seven paths to be the critical path. For example, what is the probability that Path 1 is critical? What is the probability that Path 2 is critical? And so on. Question 2 (40 marks) For the data in Question 1, perform the PERT analysis ONLY on the critical path of the project network. Determine the time for project completion with 80% and 40% probabilities. As an alternative to using tables for Z values, you can use the NORM.INV function in Excel to determine the length of the critical path for the given probability, mean (Te), and standard deviation (g) values. Comment on the differences or similarities in the results between Question 1 and Question 2