Consider a project consisting of four activities A, B, C, and D. The following are constraints within which the project has to be conducted

• A and B, the first activities of the project, can be started simultaneously.

• C can be started only after A is completed.

• D can be started only after B is completed

Suppose the activity times for the activities are A = 4 weeks, B = 3 weeks, C = 2 weeks, D = 3 weeks.

1. How long does the project take to complete?

2. We ask the engineers working on activity A to factor in uncertainty in activity times and to provide better estimates of the activity times. The engineers tell us that activity A takes 2 weeks 25% of the time, 4 weeks 50% of the time and 6 weeks 25% of the time. How long does the project now take to complete (on average)?

3. Suppose the project manager wants to be 60% certain that the project would be completed? What is deadline should they commit to?

4. We now also ask the engineer working on activity B to factor in uncertainty in activity times and to provide better estimates of the activity times. The engineer now tell us that activity B takes 2 weeks 25% of the time, and 3 weeks 50% of the time and 4 weeks 25% of the time time. How long does the project now take to complete (on average)? [ASSUME THAT BOTH ACTIVITY A AND ACTIVITY B ARE UNCERTAIN]

5. For this scenario, what deadline should they commit to that would ensure a 60% probability of completion?