Final answer:
The critical path for the given project using CPM is Path A-C-D-E-G which has the longest total duration of 31 weeks, making it the sequence of activities that determines the project's total time to completion.
Step-by-step explanation:
The question involves finding the critical path for a project using the Critical Path Method (CPM). To determine the critical path, one must calculate the earliest start time, the earliest finish time, the latest start time, and the latest finish time for each activity. The critical path is the longest duration path through the network, and activities on this path cannot be delayed without delaying the project.
By evaluating the given times for each activity, we can establish the following sequence and durations:
- A (7 weeks)
- C (A + 8 weeks)
- D (C + 3 weeks = A + 11 weeks)
- E (B + 5 weeks and D + 5 weeks, choosing the larger sum)
- F (D + 4 weeks = A + 15 weeks)
- G (E + 8 weeks and F + 8 weeks, choosing the larger sum)
By evaluating the sequences and adding up the durations, we find that:
- Path A-B-E-G has a total duration of 7(B is A + 4) + 5(E follows B or D) + 8(G follows E or F) = 20 weeks
- Path A-C-D-E-G has a total duration of 7 + 8 + 3 + 5 + 8 = 31 weeks
- Path A-C-D-F-G has a total duration of 7 + 8 + 3 + 4 + 8 = 30 weeks
Therefore, the critical path is the one with the longest duration, which is Path A-C-D-E-G (Option c).