Question 1
A project consists of the following tasks:
- Task A (Requirements Analysis): 2 days, Depends on: None
- Task B (Design): 3 days, Depends on: A
- Task C (Database Setup): 2 days, Depends on: A
- Task D (Development): 5 days, Depends on: B, C
- Task E (Testing): 3 days, Depends on: D
What is the minimum number of days required to complete the entire project?
Step-by-step solution:
Critical Path Method (CPM):
1. Identify dependencies and calculate earliest start times:
- Task A: Starts on Day 0, Duration 2 days
Finishes on Day 2
- Task B: Starts on Day 2, Duration 3 days
Finishes on Day 5
- Task C: Starts on Day 2, Duration 2 days
Finishes on Day 4
- Task D: Starts on Day 5, Duration 5 days
Finishes on Day 10
- Task E: Starts on Day 10, Duration 3 days
Finishes on Day 13
2. Task timeline:
Task A: Days 0-2
Task B: Days 2-5 (after A)
Task C: Days 2-4 (after A)
Task D: Days 5-10 (after B and C)
Task E: Days 10-13 (after D)
3. Critical path: A -> B -> D -> E (or A -> C -> D -> E)
4. Total project duration: 13 days
Key Strategy: Calculate earliest start time for each task based on predecessor completion times; the longest path determines total duration.
Critical Path Method (CPM):
1. Identify dependencies and calculate earliest start times:
- Task A: Starts on Day 0, Duration 2 days
Finishes on Day 2
- Task B: Starts on Day 2, Duration 3 days
Finishes on Day 5
- Task C: Starts on Day 2, Duration 2 days
Finishes on Day 4
- Task D: Starts on Day 5, Duration 5 days
Finishes on Day 10
- Task E: Starts on Day 10, Duration 3 days
Finishes on Day 13
2. Task timeline:
Task A: Days 0-2
Task B: Days 2-5 (after A)
Task C: Days 2-4 (after A)
Task D: Days 5-10 (after B and C)
Task E: Days 10-13 (after D)
3. Critical path: A -> B -> D -> E (or A -> C -> D -> E)
4. Total project duration: 13 days
Key Strategy: Calculate earliest start time for each task based on predecessor completion times; the longest path determines total duration.