Final answer:
Use the Critical Path Method to create an Activity On Arrow network diagram with the given project activities, identify the critical path, and calculate the project duration.
Step-by-step explanation:
The question involves using the Critical Path Method (CPM) to plan a project by developing a network diagram using the Activity On Arrow (AOA) method and identifying the critical path to determine the project's duration. To apply the CPM, one needs to analyze each activity, its predecessor(s), and the duration.
Step 1: Construct the network diagram by placing activities on arrows and connecting them from start to end. Begin with activities without predecessors and connect subsequent activities based on given precedence relationships.
Activities A and B, without predecessors, can start immediately. Activity C follows A, and Activity D also follows A. Activity E follows B, while Activity F depends on C, D, and E. Activity G follows D and E.
Step 2: After illustrating the network, identify the longest path through the network, which is the project's critical path. Calculate the duration by summing the times of activities in the critical path, determining the overall project duration.