With total float = 5 days and original duration = 10 days for an activity, what schedule flexibilities are permissible without affecting the overall project?

Introduction / Context:
Total float measures how long an activity's start or finish can be delayed without delaying the project completion (or the start of its successors, depending on conventions). Understanding float enables practical flexibility in start dates, finish dates, and even resource pacing.

Given Data / Assumptions:

• Total float (TF) = 5 days.
• Original activity duration = 10 days.
• No change to network logic or successor constraints beyond what TF already allows.

Concept / Approach:
Total float = LST - EST = LFT - EFT. If TF = 5, the activity can slip by up to 5 days in any combination of later start, later finish, or extended duration, so long as its earliest network relationships are not violated.

Step-by-Step Solution:
Option A: A 5-day delay in start still fits inside the 5-day TF.Option B: A 5-day delay in finish (holding start constant) also fits inside TF.Option C: Increasing duration from 10 to 15 days (without shifting start) delays finish by 5 days, which is exactly the available TF.Hence, all statements A, B, and C are simultaneously consistent with TF = 5.

Verification / Alternative check:
Compute TF as difference between late and early dates. Any combination of start/finish shift or duration stretch that uses ≤ 5 days of slack is permissible.

Why Other Options Are Wrong:

• Choosing only A, only B, or only C ignores other equally valid uses of the same float.

Common Pitfalls:
Confusing total float with free float; assuming float can only be used to delay start; forgetting that slower execution (longer duration) consumes float as well.

Final Answer:
All the above.