Solve the below problem:
1. In making a forward pass through a network, activities L, M, and P are immediate predecessors for activity T, which has an activity time for 7. The early start times for activities L, M, and P are 22, 17, and 27, respectively. The early finish times for activities L, M, and P are 29, 27, and 33, respectively. What is the early finish time for activity T?
2. In making a backward pass through a network, activity L has an activity time of 4 and immediately precedes activities M, P, and T. The late start times for activities M, P, and T are 22, 17, and 27, respectively. The late finish times for activities M, P, and T are 29, 27, and 33, respectively. What is the late start time for activity L?
3. Given this information about an activity: ES = 10, EF = 20, LS = 29, and LF= 39. The amount of slack associated with the activity is _______________________.
4. An activity in a network diagram has an optimistic time estimate of seven days, a most likely time estimate of 11 days, and a pessimistic time estimate of 19 days. Its variance is __________________.
5. There are four activities on the critical path, and they have standard deviations of 1, 2 ,4, and 2. The standard deviation of the critical path is _______.
6. A project being analyzed by PERT has 38 activites, 16 of which are on the critical path. If the estimated time along the critical path is 90 days with a project variance of 25, what is the probability that the project will be complete in 88 days or less?
7. Analysis of a PERT problem shows the estimated time for the critical path to be 108 days with a variance of 64, there is a .90 probability that the project will be completed before approximately day.