drakevery407
Answered

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\begin{tabular}{|l|l|l|l|l|l|l|l|}
\hline Activity & A & B & C & D & E & F & G \\
\hline Duration & 3 & 5 & 4 & 10 & 7 & 14 & 6 \\
\hline Predecessor & - & - & A & B,C & A,G & D,E & - \\
\hline
\end{tabular}

Tasks:
1. Construct the network diagram.
2. Indicate the critical path.
3. Determine the project duration.

Sagot :

GinnyAnswer
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.
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