Discuss the role of PERT, CPM and Gantt based on the following action items:

1. Identify the purpose of each tool and circumstances for using each. Also consider whether these tools are individual methods that can be used independently or if they should ideally be used as a set.

2. Contrast and compare activity-on-node and activity-on-arrow (or activity-on-arc) diagramming techniques. What are the differences and similarities?

3. Propose and describe in text form a sample project that you would theoretically develop into a PERT diagram and Gantt chart. For example, "Building a car would consist of the following steps..."(briefly outline the steps as task statements). Postulate the critical path of your sample hypothetical project: what would be the critical path sequence?