Consider the following data for a project: Immediate Normal Task predece- duration (days) Crash duration (days) Normal Crash cost cost ssors (TL) (TL) 100 1 4 2 50 2 6 4 100 500 6 4 3 1 4 2 100 400 4 4 1 1 8 5 50 300 5 2 3 3 1 200 600 6 2 7 4 4 50 200 7 4 2 300 500 8 3 3 100 100 3,5 3,5 4,7 6,8 9 5 2 200 600 10 5 4 250 300 Assume that the tasks can be performed with any duration between their Normal and Crash durations where the corresponding costs change linearly between the given Normal and Crash costs. a) (10 points) Draw the project network in AON format. Using normal durations find the earliest time the project be completed. Identify the total cost of the project, the critical activities, and ES.EF. LS.LF and slacks for each task. b) (20 points) The management wants to complete the project t days before the earliest project completion time you have found in part a. By using the intuitive approach crash the tasks so that the project will be completed t days earlier with minimum total cost for each t=1.2.3. For each day shortened identify the total cost and the tasks crashed. Tasks can be performed in any duration between their normal and crash durations and assume linear costs. For what total benefit per day, up to 3 days, it is worthwhile to finish the project earlier? When the project duration is shortened 3 days for which tasks it may be possible to increase their durations? - c) (5 points) Suppose that originally there are following additional constarints: Task 4 can start at least two days after task 3 starts. Task 9 can be completed at least 3 days after task & starts. Modify the project network with these additional constraints