. Construct a Gantt chart and project network for the following set of activities, compute the length of each path in the network, and indicate the critical path:
Activity Activity Predecessor Time (months)
1 ___ 4
2 ___ 7
3 1 8
4 1 3
5 2 9
6 3 5
7 3 2
8 4,5,6 6
9 2 5
To construct a Gantt chart and project network for the given set of activities, we need to follow these steps:
Step 1: Identify the activities and their respective predecessors.
Based on the given information, we have the following activities and their predecessors:
Activity 1: No predecessor
Activity 2: No predecessor
Activity 3: Activity 1 is the predecessor
Activity 4: Activity 1 is the predecessor
Activity 5: Activity 2 is the predecessor
Activity 6: Activity 3 is the predecessor
Activity 7: Activity 3 is the predecessor
Activity 8: Activities 4, 5, and 6 are the predecessors
Activity 9: Activity 2 is the predecessor
Step 2: Draw the project network diagram.
Based on the relationships between activities and their predecessors, we can draw the project network diagram as follows:
1 2
/ \ /
3 4 5
/ \ |
6 7 8
\ /
9
Step 3: Determine the length of each activity.
Referencing the given time (months) for each activity, we can determine the length of each activity:
Activity 1: 4 months
Activity 2: 7 months
Activity 3: 8 months
Activity 4: 3 months
Activity 5: 9 months
Activity 6: 5 months
Activity 7: 2 months
Activity 8: 6 months
Activity 9: 5 months
Step 4: Compute the length of each path in the network.
To compute the length of each path, we need to go through each path from the start node to the end node and sum up the lengths of the activities along that path. The paths in this case are:
Path 1: 1-3-6-8
Path 2: 1-3-7-8
Path 3: 1-4-8
Path 4: 2-5-8
Path 5: 2-9
Length of Path 1: 4 + 8 + 5 + 6 = 23 months
Length of Path 2: 4 + 8 + 2 + 6 = 20 months
Length of Path 3: 4 + 3 + 6 = 13 months
Length of Path 4: 7 + 9 + 6 = 22 months
Length of Path 5: 7 + 5 = 12 months
Step 5: Identify the critical path.
The critical path is the longest path in the network, as it determines the total project duration. In this case, Path 1 (1-3-6-8) is the critical path with a length of 23 months.
Finally, we can use the computed information to construct the Gantt chart, showing the start and end times of each activity along the critical path. However, since the specific starting point and duration are not mentioned, I cannot create a Gantt chart in this text-only format.