Forward and Backward Pass

Correct Answer: There is an error in the calculation as critical activities must have zero total and free float

In network diagramming and critical path analysis, a critical activity is defined by having zero total float and zero free float. This is a fundamental principle of critical path methodology. A critical activity represents the longest path through the network diagram, and by definition, any delay in a critical activity will result in a delay to the project completion date. Therefore, having both total float (5 days) and free float (3 days) on what is claimed to be a critical activity indicates a calculation error. Total float is the amount of time an activity can be delayed before impacting the project completion date, while free float is the amount of time an activity can be delayed before impacting the early start of a successor activity. For a critical activity, both these values must be zero. If an activity has any float (total or free), it means there is slack time available, which by definition makes it a non-critical activity. Therefore, this scenario presents a mathematical impossibility in critical path calculations, indicating there must be an error in the computations.

Correct Answer: The activity has a total float of 5 days

The difference between Late Start (LS) and Early Start (ES) indicates the total float of an activity. In this case: LS = Day 10 ES = Day 5 Total Float = LS - ES = 10 - 5 = 5 days This means the activity can start anywhere between Day 5 and Day 10 and still meet the project schedule constraints. The float provides flexibility in scheduling. The other answers are incorrect because: - The duration of the activity is not shown by this information - we only know its start time flexibility - Critical path activities have zero float, which is not the case here - Resource requirements cannot be determined from ES and LS times alone

Correct Answer: Activity C lies on the critical path

When an activity's Early Finish (EF) equals its Late Finish (LF), it indicates zero total float. Zero total float is the defining characteristic of activities on the critical path. In this case: EF = Day 15 LF = Day 15 Total Float = LF - EF = 0 This equality between EF and LF means Activity C must be completed exactly as scheduled, with no flexibility in its timing, which is the hallmark of a critical path activity. The other answers are incorrect because: - Maximum schedule flexibility would require a significant difference between EF and LF, not equality - A parallel path with float would show different EF and LF values - Standard buffer time would also show a difference between EF and LF times, not equality