In a CPM (Critical Path Method) network, the critical path refers to the sequence of activities that determines the total duration of the project. It is the longest path through the network and represents the minimum time required to complete the project.

The critical path is determined based on the dependencies and durations of each activity in the project. Activities are represented by nodes in the network, and the arrows between the nodes indicate the dependencies between them. The duration of each activity is also specified.

Now, let's discuss the options given in the question and why option 'C' is the correct answer:

a) Path where maximum resources are used:
The critical path does not necessarily involve the maximum utilization of resources. It is possible that activities on the critical path require fewer resources compared to other paths in the network.

b) Path where minimum resources are used:
Similar to the previous option, the critical path does not focus on minimizing resource utilization. It is primarily concerned with determining the duration of the project based on the dependencies and durations of activities.

c) Path where delay of one activity prolongs the duration of completion of the project:
This is the correct answer. The critical path is the one where any delay in the completion of an activity will directly impact the overall project completion time. Each activity on the critical path has zero total float, which means there is no flexibility or slack in their scheduling. Any delay in these activities will extend the project duration.

d) Path that gets monitored automatically:
While the critical path is an important aspect of project management, it does not necessarily mean that it gets monitored automatically. Monitoring the critical path requires tracking the progress of activities, identifying any delays or bottlenecks, and making necessary adjustments to ensure timely project completion.

Overall, the critical path plays a crucial role in project planning and scheduling. It helps project managers to identify the activities that are most critical to the project's duration and ensure that they are completed on time to prevent project delays.