Consider the following network of activities, with each activity named A–L, illustrated in the nodes of the network.

The number of hours required for each activity is shown alongside the nodes. The slack on the activity L, is ________ hours.

The correct answer is : 2

Step-by-step Explanation:

To find the slack on activity L, we must first analyze the project network diagram shown in the image. From the diagram, we can identify all possible paths from the "Start" node to the "Finish" node, along with the durations (in hours) indicated next to each activity node:
- Node A: 2 hours
- Node B: 4 hours
- Node C: 10 hours
- Node D: 6 hours
- Node E: 4 hours
- Node F: 7 hours
- Node G: 7 hours
- Node H: 9 hours
- Node I: 8 hours
- Node J: 5 hours
- Node K: 6 hours
- Node L: 2 hours

Now, let's identify the three distinct paths through the network from Start to Finish and calculate their total durations:

Path 1: A - B - C - F - I - J - K

$\text{Duration}=2+4+10+7+8+5+6=42\text{hours}$

Since Path 1 is the longest path in the network, it defines the critical path. Therefore, the minimum project completion time is 42 hours.

Path 2: A - B - C - E - H - L

$\text{Duration}=2+4+10+4+9+2=31\text{hours}$

Path 3: A - B - C - D - G - H - L

$\text{Duration}=2+4+10+6+7+9+2=40\text{hours}$

Activity L lies on both Path 2 and Path 3. To find the slack (or float) on activity L, we determine how much we can delay this branch without delaying the overall project completion time. The longest path containing activity L is Path 3 with a duration of 40 hours.

The slack for activity L is calculated as the difference between the project completion time (critical path duration) and the duration of the longest path that includes activity L:

$\text{Slack for L}=\text{Critical Path Duration}-\text{Duration of Path 3}$

$\text{Slack for L}=42-40=2\text{hours}$

Thus, the slack on activity L is 2 hours.