Slack on various events at critical path on a PERT/CPM chart remains constant because:

Explanation:
PERT/CPM charts are used to manage and schedule complex projects. The critical path is the longest path in the network diagram, which determines the minimum time required to complete the project. Slack is the amount of time an activity can be delayed without delaying the project completion time. The events on the critical path have zero slack, which means any delay in these events will delay the project completion time.

The slack on various events at critical path remains constant because of the following reasons:

1. Critical Path:
The events on the critical path have zero slack, which means any delay in these events will delay the project completion time. As the slack is zero, it remains constant throughout the project.

2. Fixed duration:
The duration of the events on the critical path is fixed and cannot be changed without delaying the project completion time. Hence, the slack on these events remains constant.

3. Resource allocation:
The resources required for the events on the critical path are allocated in such a way that the duration of the events is minimized. This results in zero slack on these events, which remains constant.

4. Time management:
The project manager closely monitors the events on the critical path to ensure that they are completed on time. Any delay in these events will delay the project completion time, which is undesirable. Hence, the slack on these events remains constant.

Conclusion:
Hence, it can be concluded that the slack on various events at critical path on a PERT/CPM chart remains constant because the events on the critical path have zero slack, the duration of the events is fixed, the resources are allocated efficiently, and the project manager closely monitors the events to ensure on-time completion.