Consider the following activity-on-arc project network, where the 12 arcs (arrows) represent the 12 activities (tasks) that must be performed to complete the project and the network displays the order in which the activities need to be performed. The number next to each arc (arrow) is the time required for the corresponding activity. Consider the problem of finding the longest path (the largest total time) through this network from start (node 1) to finish (node 9), since the longest path is the critical path.

(a) Formulate the network flow model for the corresponding diagram.

(b) What is the logical resoning behind the fact that the longest path in a network is chosen to be the critical path.

Figure 1