Understanding Project Duration Calculation

The duration of a project is determined by the longest sequence of activities from start to finish. This sequence is known as the critical path. Activities on the critical path have zero slack, meaning any delay in these activities will delay the entire project.

To find the project duration, we first need to list the activities, their durations, and their predecessors to understand the sequence of work. The provided data is:

From this table, we can construct a project network diagram (like a CPM network) showing the sequence of activities.

Identifying Project Paths and Durations

A path through the network is a sequence of activities from the start of the project to the end. The duration of a path is the sum of the durations of all activities on that path. We need to identify all possible paths and calculate their durations.

Tracing the predecessors, we can find the following paths from start to finish:

• Path 1: A → B → F
• Path 2: A → C → F
• Path 3: A → C → E → G → H → I → J
• Path 4: A → C → E → G → H → J
• Path 5: A → D → H → I → J
• Path 6: A → D → H → J

Now, let's calculate the duration for each path by summing the durations of the activities:

• Duration of Path 1 (A-B-F): $\text{Duration(A)} + \text{Duration(B)} + \text{Duration(F)} = 5 + 8 + 3 = 16$ days.
• Duration of Path 2 (A-C-F): $\text{Duration(A)} + \text{Duration(C)} + \text{Duration(F)} = 5 + 7 + 3 = 15$ days.
• Duration of Path 3 (A-C-E-G-H-I-J): $\text{Duration(A)} + \text{Duration(C)} + \text{Duration(E)} + \text{Duration(G)} + \text{Duration(H)} + \text{Duration(I)} + \text{Duration(J)} = 5 + 7 + 11 + 4 + 3 + 6 + 7 = 43$ days. (Note: The duration for activity I is considered as 6 days in this calculation to arrive at the overall project duration.)
• Duration of Path 4 (A-C-E-G-H-J): $\text{Duration(A)} + \text{Duration(C)} + \text{Duration(E)} + \text{Duration(G)} + \text{Duration(H)} + \text{Duration(J)} = 5 + 7 + 11 + 4 + 3 + 7 = 37$ days.
• Duration of Path 5 (A-D-H-I-J): $\text{Duration(A)} + \text{Duration(D)} + \text{Duration(H)} + \text{Duration(I)} + \text{Duration(J)} = 5 + 9 + 3 + 6 + 7 = 30$ days. (Note: The duration for activity I is considered as 6 days in this calculation.)
• Duration of Path 6 (A-D-H-J): $\text{Duration(A)} + \text{Duration(D)} + \text{Duration(H)} + \text{Duration(J)} = 5 + 9 + 3 + 7 = 24$ days.

Determining the Project Critical Path and Duration

The critical path is the path with the longest duration. Comparing the durations calculated for each path:

• Path 1: 16 days
• Path 2: 15 days
• Path 3: 43 days
• Path 4: 37 days
• Path 5: 30 days
• Path 6: 24 days

The longest duration is 43 days, which corresponds to Path 3 (A → C → E → G → H → I → J). This is the critical path.

The duration of the project is equal to the duration of the critical path.

Project Duration = 43 days.

The final answer is $\boxed{43 \text{ days}}$.