2. (30 points) The table below lists the activity times and precedence requirements for the activities required to complete a new equipment installation project in a factory. Three time estimates (in weeks) are given for each activity: optimistic time, most likely time, and pessimistic time. (a) Draw the PERT network diagram for the project, labeling all activities and times. (b) Perform a forward pass and backward pass through the network to determine the critical path, the expected duration of the project, and the slack time for each activity. (c) What is the probability that the project will be completed one week or more before the expected completion time? Activity Optimistic time (weeks) Most likely time (weeks) Pessimistic time (weeks) Immediate predecessor 1 0 0 0 2 3 5 7 1 3 5 6 9 1 4 3 5 6 2 5 4 7 10 3 6 5 8 10 3 7 6 10 12 4 8 3 4 6 5 9 5 9 13 5 10 1 2 3 6 11 3 7 10 12 1 5 6 7,8 9, 10 11, 12 13 0 0 0