Sure! Let's work through the steps to construct the network diagram, indicate the critical path, and determine the project duration. Here's the problem broken down into its components:
### 1. Construct the Network Diagram:
To construct a network diagram, we need to represent each activity and its dependencies.
- Activity A has no predecessors.
- Activity B has no predecessors.
- Activity C depends on A.
- Activity D depends on B and C.
- Activity E depends on A and G.
- Activity F depends on D and E.
- Activity G has no predecessors.
We'll connect each activity to its successors to show the dependencies:
```
Start --> A --> C --> D --> F --> End
| |
|--> E --> F --|
|
B --> D --> F
|
G --> E --> F
```
### 2. Indicate the Critical Path:
The critical path is the longest path through the network diagram. We need to find all paths and calculate their durations.
Here's the process:
- Identify all possible paths from start to finish.
- Calculate the total duration of each path.
- The path with the longest duration is the critical path.
Considering the dependencies, potential paths could be:
1. Start -> A -> C -> D -> F -> End
2. Start -> B -> D -> F -> End
3. Start -> A -> E -> F -> End
4. Start -> G -> E -> F -> End
Next, we calculate the duration for each path:
1. Start -> A -> C -> D -> F -> End:
- A (3) + C (4) + D (10) + F (14) = 31
2. Start -> B -> D -> F -> End:
- B (5) + D (10) + F (14) = 29
3. Start -> A -> E -> F -> End:
- A (3) + E (7) + F (14) = 24
4. Start -> G -> E -> F -> End:
- G (6) + E (7) + F (14) = 27
Now we compare the durations:
- Path 1: 31
- Path 2: 29
- Path 3: 24
- Path 4: 27
The longest duration is 31, so the critical path is:
A -> C -> D -> F
### 3. Determine the Project Duration:
The duration of the project is the total duration of the critical path.
The project duration is 31 units of time.
### Summary:
- The critical path is A -> C -> D -> F.
- The project duration is 31 units of time.
