The first image you provided shows a project network diagram, with tasks represented by nodes and their durations labeled on the connecting arrows. The second image includes a partial table of early finish times (EFT) for the tasks and blank columns for the late start times (LST).

Let's solve the missing entries in your table using the Critical Path Method (CPM). Here's the approach:

Key Definitions:

• Early Finish Time (EFT): The earliest time by which a task can be completed.
• Late Start Time (LST): The latest time a task can start without delaying the project.

Steps:

1. Forward Pass:

   • Calculate the early start (ES) and early finish (EF) for each task, based on the sequence of tasks and durations.

2. Backward Pass:

   • Calculate the latest start (LS) and latest finish (LF) for each task, by working backwards from the end of the project to determine slack times.

Forward Pass (Given Data):

• B (1 → 2): EFT = 7
• C (1 → 3): EFT = 5
• D (3 → 5): EFT = 10
• E (2 → 4): EFT = 12
• F (4 → 6): EFT = 23
• G (4 → 7): EFT = 20
• H (5 → 8): EFT = 25

Calculations for Backward Pass:

• The latest finish for the entire project is determined by the longest path to the end. From the diagram:
  • The path $1 \to 2 \to 4 \to 6$ gives a total time of $7 + 5 + 11 = 23$.
  • The path $1 \to 2 \to 4 \to 7 \to 9$ gives $7 + 5 + 8 + 7 = 27$.
  • The path $1 \to 3 \to 5 \to 8 \to 9$ gives $5 + 3 + 13 + 5 = 26$.
  • Therefore, the latest finish time for the project is 27.

Next, I'll calculate the LST for each task based on this latest finish time and update the table.The Late Start Times (LST) for the tasks have been calculated as follows:

• B (1 → 2): LST = 20
• C (1 → 3): LST = 22
• D (3 → 5): LST = 24
• E (2 → 4): LST = 22
• F (4 → 6): LST = 16
• G (4 → 7): LST = 19
• H (5 → 8): LST = 14

Would you like further details on how these calculations were performed or have any other questions?

Here are 5 related questions:

1. How do Early Start Times (EST) relate to Early Finish Times (EFT)?
2. What is the critical path in this network diagram?
3. How do we determine the slack time for each task?
4. Why is the latest finish time of the project set to 27?
5. What happens if one task is delayed in a project network?

Tip: Understanding the critical path can help identify tasks that must be completed on time to avoid project delays.