Critical Path Method (CPM)

Correct Answer: A, B, C, D, E

To identify the critical path, we need to consider the dependencies and the fact that the critical path is the longest duration path through the project, determining the project's shortest completion time. - Tasks A and B are parallel; their completion is required before starting Task C. - Task C can start only after both A and B are completed. - Task D can start only after C is complete. - Task E can start after either Task B or D is done. Given these dependencies, the critical path must include Task C because it requires the completion of both A and B. After C, Task D must be completed before E can start, based on the requirement that D must be done before E. So, even though E can start after B is done, the dependency of E on D (which in turn depends on C, which depends on both A and B) makes A-B-C-D-E the sequence that dictates the project's minimum completion time. Thus, the critical path is A, B, C, D, E.

Correct Answer: Increase by 3 days

In the given scenario, tasks are dependent on one another. The project's critical path is determined by the sequence of tasks that must occur from start to finish, where the delay of any task will delay the completion of the entire project. The sequence for this project will be: Task A > Task B > Task D and Task A > Task C. Task A needs to be completed first before Task B and Task C can start. Task D can only begin when Task B is completed. If Task A is delayed by 3 days, it means that the start of Tasks B and C will also be postponed by 3 days. Therefore, the total time for the project will increase by 3 days because the delay in Task A affects the start of the other tasks. The answer 'Remains unchanged' is incorrect because a delay in the initial task in a critical path will always affect the total project time. The answer 'Decrease by 3 days' is wrong as delay only leads to an increase in time taken and not decrease. Finally, the answer 'Increase by 4 days' is also wrong because the delay specified is 3 days, so the increase in critical path duration will be exactly equal to the delay.

Correct Answer: Delay the project by 3 days

The project's critical path is initially B-C-D, totaling 13 days (3+4+6). Task A (5 days) runs parallel to B and C, finishing before D starts. When B is delayed by 3 days, it extends to 6 days, making the new critical path 16 days (6+4+6). This results in a 3-day delay to the overall project duration. Task A still finishes within this timeframe and does not affect the critical path.