Assume you have been recently hired as a systems engineering manager. One of the main goals in your new position is to streamline the design and development process and improve scheduling. As such, you wish to perform PERT analysis and critical path management for each project under your supervision. In critical path management, a schedule of events or tasks is listed and sequential dependencies between events are identified. In this context, the critical path is the path of sequentially dependent events that has the longest total time (aggregation of time for all events in the sequence). You decide to represent the events including their estimated times and sequential dependencies using a directed graph.

Describe how you would construct such a graph. What do the nodes represent? What do the edges represent? What values would the weights represent? Is this graph a tree? Is this graph directed or undirected? Justify this design.

Suppose you wish to identify the critical path. What type of path is this? Describe and name the type of path within the context of the graph. Explain how you will use graphs and graph-based methods to find the critical path. Justify your answer.

Create an example graph that has at least five events and at least seven dependencies. Identify the critical path.