A project manager has collected the following information for her new software application project to create a customer database. Duration (Day) Activity ID Activity Description Predecessor Optimistic Most Likely Pessimistic A Systems design 6 8 10 B Subsystem A design A 1 2 3 C Subsystem B design A 1 3 5 D Subsystem C design A 40 60 E Program A B 30 40 50 F Program B C 1 2 3 G Program C D 1 2 3 H Subsystem A test E, F 15 20 25 Subsystem B test G 5 10 15 J Subsystem C test H, I 5 10 15 K Integration J 6 12 18 L Integration test K 1 3 5 a) Develop the project network diagram. b) Complete the forward and backward pass, and compute activity slack. Use PERT techniques for project activities duration. c) Compute the project duration and identify the critical path. d) Compute the probability the project will be done in 108 days. e) With a probability of 90%, how long does the project take