If TL denotes the latest allowable occurrence time of the head event, the total activity slack (total float) is equal to which of the following expressions?

Introduction / Context:
Total float quantifies the maximum delay allowable for an activity without jeopardizing the project schedule. Multiple equivalent expressions exist depending on whether we look at starts, finishes, or event times.

Given Data / Assumptions:

• EST/EFT: earliest start/finish times of the activity.
• LST/LFT: latest start/finish times consistent with project deadlines.
• TL: latest allowable time of the head (finish) event connected to the activity.

Concept / Approach:
Total float TF can be written in equivalent ways: TF = LST - EST = LFT - EFT. In Activity-on-Arrow, with TL as latest time of the head event, TF can also be expressed as TF = TL - EFT, since the head event's latest time bounds the latest feasible finish of the activity.

Step-by-Step Solution:
Start definition: TF = LST - EST.Using durations, TF equivalently equals LFT - EFT.With event times, TF equals TL - EFT for the head event, maintaining consistency.Therefore, all listed expressions are valid and equal.

Verification / Alternative check:
Compute with a small example network and confirm the equality numerically; each form yields identical TF values.

Why Other Options Are Wrong:

• Any single expression alone is not wrong, but choosing only one ignores the other equivalent forms.

Common Pitfalls:
Mixing up free float and total float; misapplying TL (event time) as if it were LFT without linking to the head event.

Final Answer:
All the above.