Final answer:
To calculate project duration and the critical path, an AON network diagram is drawn from the logic table. Crashing activities on the critical path reduce the duration economically, with each crash analyzed for project cost and duration changes. Without specific data, we can provide only a procedural overview.
Step-by-step explanation:
To calculate the normal project duration and identify the critical path, one must draw an Activity-On-Node (AON) network diagram based on the logic table provided. The critical path is the sequence of project network activities which add up to the longest overall duration, and this is the path that determines the shortest time possible to complete the project. After this, a crashing exercise can be done to reduce project duration economically.
Crashing involves reducing project time by applying additional resources to project activities, with a cost. To find the most economical method to reduce the project duration by 4 weeks, we must look at the activities on the critical path and their respective crash costs and durations. One should crash the least expensive activity per unit of time first and then reassess the critical path after each crash because it might change. The project duration, cost, and new critical path(s) should be reported after each crash.
At every step of crashing, it is essential to review the recalculated project costs and the duration against the scenario before crashing. This stepwise approach allows for effective project management and optimization of resource allocation. Usually, you would have specific data to work with, but since the question is hypothetical, we cannot perform actual calculations without the logic table or crash data.