Question

The network diagram of eight activities (A to H) along with their time durations (in days, given in bracket) of a project is shown in the figure. The critical path of the project is: 

• A. \( 1 \to 2 \to 3 \to 6 \)
• B. \( 1 \to 4 \to 3 \to 6 \)
• C. \( 1 \to 5 \to 6 \)
• D. \( 1 \to 4 \to 5 \to 6 \)

Hint:

The critical path method (CPM) is used to determine the longest path through the project network. The longest path determines the minimum project duration, and any delay in the critical path will directly affect the project’s completion time.

Answer 1

The Correct Option is B

To find the critical path, we first need to calculate the total durations for each possible path in the network and identify the longest path, which determines the project duration. Let's go step by step:
1. Path 1: \( 1 \to 2 \to 3 \to 6 \)
- Duration: \( A (3) + D (5) + G (6) = 3 + 5 + 6 = 14 \) days.
2. Path 2: \( 1 \to 4 \to 3 \to 6 \)
- Duration: \( A (3) + E (7) + D (5) + G (6) = 3 + 7 + 5 + 6 = 21 \) days.
3. Path 3: \( 1 \to 5 \to 6 \)
- Duration: \( A (3) + F (1) + G (6) = 3 + 1 + 6 = 10 \) days.
4. Path 4: \( 1 \to 4 \to 5 \to 6 \)
- Duration: \( A (3) + E (7) + F (1) + G (6) = 3 + 7 + 1 + 6 = 17 \) days.
Now, comparing the total durations, we find that Path 2, \( 1 \to 4 \to 3 \to 6 \), has the longest duration of 21 days, which means it is the critical path.
Thus, the critical path is \( 1 \to 4 \to 3 \to 6 \) and the correct answer is (B).