---
title: "CPM network, 9 activities (A=3 to I=1)"
subject: "Project Engineering"
chapter: 3
key: "semester_7/project_engineering:cpm-network-nine-act-b82"
source: https://www.bctengineer.com/q/semester_7/project_engineering/cpm-network-nine-act-b82
site: BCT Engineering
---

# CPM network, 9 activities (A=3 to I=1)

Project Engineering · Chapter 3: Project Planning and Scheduling

- Asked in: 2082 Bhadra, 14 marks; 2074 Chaitra, 12 marks (asked 2 times)
- Video: [Use forward and backward pass to determine project duration and critical path](https://www.youtube.com/watch?v=4oDLMs11Exs) — Engineer4Free
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/project_engineering/cpm-network-nine-act-b82
- Whole chapter: https://www.bctengineer.com/md/semester_7/project_engineering/chapter-3

## Question

Draw the CPM network diagram and compute EST, EFT, LST, LFT, TF, FF, Int.F and Ind.F from the information given below. Also compute the project duration and mark the critical path.

| Activity | Duration (week) | Predecessor |
|---|---|---|
| A | 3 | - |
| B | 2 | - |
| C | 0 | A |
| D | 4 | A |
| E | 7 | B, C |
| F | 5 | B, C |
| G | 8 | D, E |
| H | 6 | F |
| I | 1 | G, H |

## Short answer

Forward and backward pass on activity-on-arrow network yields project duration 19 weeks. Critical path: A-C-E-G-I.

## Answer

#### Network diagram (activity on arrow)
Events are numbered 1 to 7. Activity C has zero duration, so event 3 is reached when both A (via C) and B finish. Event times (EST = LST) are: 1: 0, 2: 3, 3: 3, 4: 10, 6: 18, 7: 19; event 5 has EST 8 and LST 12.

```text
         +------D4-------+
         |               v
(1)-A3->(2)-C0->(3)-E7->(4)-G8->(6)-I1->(7)
 |              ^ |              ^
 +-----B2-------+ +-F5->(5)-H6---+
```

Event 4 follows D and E, event 6 follows G and H, and event 7 is the end.

#### Forward pass (EST, EFT)
$EST$ = largest $EFT$ of predecessors; $EFT = EST + D$.

#### Backward pass (LFT, LST)
$LFT$ = smallest $LST$ of successors; $LST = LFT - D$. Project duration $T = 19$ weeks.

#### Floats
$TF = LST - EST$; $FF = \min(EST\ \text{of successors}) - EFT$; $Int.F = TF - FF$; $Ind.F = \max\{0, \min(EST\ \text{of successors}) - \max(LFT\ \text{of predecessors}) - D\}$.

| Act | D | EST | EFT | LST | LFT | TF | FF | Int.F | Ind.F | Critical |
|---|---|---|---|---|---|---|---|---|---|---|
| A | 3 | 0 | 3 | 0 | 3 | 0 | 0 | 0 | 0 | Yes |
| B | 2 | 0 | 2 | 1 | 3 | 1 | 1 | 0 | 1 | No |
| C | 0 | 3 | 3 | 3 | 3 | 0 | 0 | 0 | 0 | Yes |
| D | 4 | 3 | 7 | 6 | 10 | 3 | 3 | 0 | 3 | No |
| E | 7 | 3 | 10 | 3 | 10 | 0 | 0 | 0 | 0 | Yes |
| F | 5 | 3 | 8 | 7 | 12 | 4 | 0 | 4 | 0 | No |
| G | 8 | 10 | 18 | 10 | 18 | 0 | 0 | 0 | 0 | Yes |
| H | 6 | 8 | 14 | 12 | 18 | 4 | 4 | 0 | 0 | No |
| I | 1 | 18 | 19 | 18 | 19 | 0 | 0 | 0 | 0 | Yes |

Sample check, activity F: $EST = \max(EFT_B, EFT_C) = \max(2,3) = 3$; $EFT = 8$; $LFT = LST_H = 12$; $LST = 7$; $TF = 7-3 = 4$; $FF = EST_H - EFT_F = 8-8 = 0$; $Int.F = 4$.

**Answer:** Project duration = **19 weeks**. Critical path: **A - C - E - G - I** ($3+0+7+8+1 = 19$).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Project duration is:
   A. 17 weeks
   B. 19 weeks
   C. 21 weeks
   D. 18 weeks
   Answer: B. A-C-E-G-I = 3+0+7+8+1 = 19. (Key point: Duration)

2. Critical path is:
   A. B-F-H-I
   B. A-D-G-I
   C. A-C-E-G-I
   D. A-C-F-H-I
   Answer: C. These have TF = 0 and sum to 19. (Key point: Critical path)

3. TF of F is:
   A. 0
   B. 3
   C. 4
   D. 7
   Answer: C. TF = LST - EST = 7 - 3 = 4. (Key point: Total float)

4. FF of D is 3 because:
   A. EST of G minus EFT of D = 10 - 7
   B. LST - EST = 3 only
   C. 8 - 5
   D. TF minus FF
   Answer: A. FF = min EST of successor - EFT = 10 - 7 = 3. (Key point: Free float)

## Close variants set in other exams

- [CPM network, 9 activities (A=5 to I=2)](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Acpm-network-nine-act-a75) — Project Engineering, chapter 3, asked 5×
- [CPM network, 13 activities (A to M)](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Acpm-network-thirteen-act-k82) — Project Engineering, chapter 3, asked 5×
- [CPM network, 13 activities (A=2 to M=7)](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Acpm-network-thirteen-act-b81) — Project Engineering, chapter 3, asked 5×

## Related in Project Engineering

- [CPM network, 12 activities (A=10 to L=8)](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Acpm-network-twelve-act-as67) — Project Engineering, chapter 3
- [CPM network, 12 activities (A=8 to L=3)](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Acpm-network-twelve-act-b66) — Project Engineering, chapter 3
- [CPM network, 10 activities (A=4 to J=9)](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Acpm-network-ten-act-as70) — Project Engineering, chapter 3
- [CPM network, 10 activities with successors](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Acpm-network-ten-act-a74) — Project Engineering, chapter 3
- [CPM network, 10 activities (A=10 to J=4)](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Acpm-network-ten-act-k79) — Project Engineering, chapter 3
- [CPM network, building project (A to K)](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Acpm-network-eleven-act-s73) — Project Engineering, chapter 3

## Related in other subjects

- [CPM schedule, critical path and float](https://www.bctengineer.com/question.md?key=semester_6%2Findustrial_engineering_and_management%3Acpm-network-critical-path-float) — Industrial Engineering and Management, chapter 3