The correct answer is: A. Free float of the activity must be zero but independent float need not be zero.
Free float is the amount of time that an activity can be delayed without delaying the start of any succeeding activities. Independent float is the amount of time that an activity can be delayed without delaying the project completion date.
When an activity has zero total float, it means that the activity is on the critical path. The critical path is the sequence of activities that determines the earliest possible completion date for the project. Any delay on any activity on the critical path will delay the project completion date.
The free float of an activity on the critical path is zero, because any delay to the activity will delay the start of succeeding activities, and therefore delay the project completion date. However, the independent float of an activity on the critical path may not be zero. This is because the independent float is calculated based on the earliest start time of the activity, which may be earlier than the actual start time of the activity. For example, if an activity has an earliest start time of 10 days and a duration of 5 days, then the independent float is 5 days. However, if the activity is actually started on day 15, then the independent float will be zero.
In conclusion, when an activity has zero total float, the free float of the activity must be zero but the independent float need not be zero.