If the value of p is 3 weeks, what will be the ﬂoat time, in weeks, of activity G.

To determine the float time of activity \( G \) when \( p = 3 \) weeks, we need to go through the following steps:

### Step 1: Identify the Critical Path

First, we need to calculate the total duration of each path with \( p = 3 \) weeks. The paths are:

1. **Path 1**: \( A \to H \to G \to J \to Finish \)
2. **Path 2**: \( B \to D \to G \to J \to Finish \)
3. **Path 3**: \( C \to F \to I \to J \to Finish \)

### Step 2: Calculate Durations

Let's calculate the total time for each path:

- **Path 1**: \( A (10) + H (3) + G (12) + J (p) = 10 + 3 + 12 + 3 = 28 \) weeks
- **Path 2**: \( B (4) + D (5) + G (12) + J (p) = 4 + 5 + 12 + 3 = 24 \) weeks
- **Path 3**: \( C (6) + F (9) + I (2) + J (p) = 6 + 9 + 2 + 3 = 20 \) weeks

### Step 3: Determine the Critical Path
- The critical path is Path 1, with a total duration of 28 weeks.

### Step 4: Calculate Earliest Start and Latest Start for \( G \)

- **Earliest Start of \( G \)**: \( G \) starts after \( H \) and \( D \) are completed. The earliest start time for \( G \) is after \( D \) finishes, which is \( 9 \) weeks.
- **Latest Start of \( G \)**: The latest start of \( G \) would be the total project duration minus the time after \( G \) is completed on Path 1.

  Latest Start of \( G = \) Project duration \(- J\)'s duration  \(= 28 - 3 = 25 \) weeks.

### Step 5: Calculate the Float Time for \( G \)

The float time is the difference between the latest start time and the earliest start time.

\[
\text{Float time for } G = 25 - 9 = 16 \text{ weeks}
\]

Thus, the float time for activity \( G \) when \( p = 3 \) weeks is **16 weeks**.

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Would you like any further details or have other questions on this problem?

Here are five related questions:
1. What is the significance of identifying the critical path in project management?
2. How does changing the value of \( p \) affect the overall project schedule?
3. What would happen if the value of \( p \) was increased to 4 weeks?
4. How can float time be used in managing project schedules?
5. What are the implications if an activity on the critical path is delayed?

**Tip:** Understanding float time can help project managers allocate resources more effectively and identify which tasks can be delayed without affecting the overall project timeline.

Learn how to calculate the float time for activity G in project management when the project duration is known. This problem involves using the Critical Path Method to determine the critical path and calculate float times for project activities. Suitable for project managers and students studying project management concepts.

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