Final answer:
The critical path for the project is A - 7. The expected project completion time is 7 units of time. Slack for activity A is 0, since it is on the critical path and cannot be delayed without delaying the project.
Step-by-step explanation:
The critical path of a project represents the sequence of activities that must be completed in order for the project to finish on time. In this case, the critical path can be determined by identifying the longest path through the project network diagram. The critical path for this project is A - 7. The expected project completion time can be calculated by adding the durations of the activities along the critical path. In this case, the expected project completion time is 7 units of time.
Slack is the amount of time an activity can be delayed without delaying the project. To determine the slack for each activity, subtract the duration of the activity from the total time available for the activity. In this case, the slack for activity A is 0, since it is on the critical path and cannot be delayed without delaying the project.
Optimizing resource allocation involves assigning resources in a way that minimizes the project's duration or cost. This can be done by identifying bottlenecks and allocating additional resources to those activities, or by adjusting the sequence of activities to make better use of available resources.