The district magistrate of a city has decided to reconstruct the most frequented street of the city. He plans to block the street for the duration of the work, which will cause considerable inconvenience to the people of the city. The project has three parallel paths defined as the following:
Path A-B-C-H will take 16 days.
Path A-D-E-H will take 22 days.
Path A-F-G-H will take 30 days.
In the given scenario, which of the following statements is true?
A) The expected duration of the project is 68 days.
B) Activities B, D, and F have an earliest starting time of 0.
C) Path A-D-E-H has the largest slack time.
D) Path A-F-G-H is the critical path.

Question

Quizplus · Accepted Answer

In a project network diagram, the critical path refers to the longest path with the least amount of slack time. Here, Path A-F-G-H is the only path which takes 30 days and has no slack time. So, if any activity on this path gets delayed, the whole project will be delayed. Therefore, the correct answer is D.

Option A is incorrect because the expected duration of the project is the sum of the duration of the critical path, which is 30 days, not the sum of the duration of all paths (which is 68 days).

Option B is incorrect because the earliest starting time of an activity is determined by the completion time of all its predecessor activities, and we don't have that information.

Option C is incorrect because slack time is the time by which an activity can be delayed without delaying the project, and it is calculated by subtracting the activity duration from the difference between the early and late start times. So, the path with the largest slack time would be the one with the most activities that can be delayed without delaying the project, and we don't have that information.

The District Magistrate of a City Has Decided to Reconstruct