4. A software company is planning a new software development. The table below lists three time estimates and the immediate predecessor(s) for each activity in the development of this software. The three time estimates (in weeks) are in the order: 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 within 22 weeks? (d) Using MS Project software construct a Gantt chart for this project. Activity 1 2 3 5 Time estimates (weeks) 1,2,3 2,4,6 3,5,7 5,7,12 5,7,9 2,3,4 6,9,12 1, 3,8 Immediate predecessor 4,5 4 6 7 8 1 1 2 3 3 6,7