Question 3.2 (15 points). The table below provides the work breakdown structure, precedence (sequential) relationships among project activities, normal and crash activity times (durations), and the normal and crash costs for a project. (a) Sketch an activity-on-node (AON) precedence network diagram for the project (4 marks). (b) Complete a forward and backward pass to determine the critical path. Identify the critical path, state how long it will take to complete the project without crashing, and what the total cost of the project will be (4 marks). (c) Calculate the slack for each activity, and the path slack for each path in the project network (3 marks). (d) Which activities would you shorten (crash) and by how much in order to reduce the total time it takes to complete the project by 4 weeks with the minimum amount of additional cost? For activities that can be crashed more than 1 week, assume the activities can be crashed in one-week increments (i.e. they do not need to be crashed the total number of weeks possible, they can be crashed 1 week at a time). (4 marks) Activity Immediate Predecessors Normal Time (weeks) Crash Time Normal Cost Crash Cost (per week) A None 7 6 $7000 $1000 B A 2 1 5000 2000 A 4 3 9000 1200 D B, C 5 4 3000 1500 E 3 2 2000 3000 F D 4 2 4000 3500 G D, E 3 1 6000 1600 H F, G 5 3 5000 1500