Floats in network analysis – identify the incorrect statement Which of the following statements about total float and free float is incorrect?

Introduction / Context:
Understanding float types is essential to manage schedule flexibility. Total float indicates how long an activity may be delayed without affecting the project completion, while free float indicates how long it may be delayed without affecting the earliest start of any successor.

Given Data / Assumptions:

• EST, EFT denote earliest start and finish; LST, LFT denote latest start and finish.
• Activity duration is denoted by d.

Concept / Approach:
Key formulas in conventional notation are:

• Total float TF = LFT - EFT = LST - EST = (LFT - EST) - d.
• Maximum time available for the activity = LFT - EST.
• Free float FF = min(EST of successors) - EFT (for a single successor, FF = EST_successor - EFT).

Step-by-Step Solution:
Check (a): LFT - EST indeed represents the maximum span available; correct.Check (b): (LFT - EST) - d equals TF; correct.Check (c): LST - EST equals TF; correct.Check (d): Free float is computed as EST of successor minus EFT of the activity; the statement matches this relationship; correct.Therefore no statement is incorrect → choose 'None of these'.

Verification / Alternative check:
Create a small two-activity chain: A (d=4) → B; let EST(A)=0, EFT(A)=4, EST(B)=6, LFT(A)=10. Then TF(A) = 10 - 4 = 6, also LST - EST = 6, and FF(A) = 6 - 4 = 2, validating the formulas.

Why Other Options Are Wrong:
Options (a)–(d) are correct statements; only picking one as 'incorrect' would contradict standard definitions.

Common Pitfalls:
Mixing up EST/EFT with LST/LFT; forgetting to subtract duration when moving from 'maximum available time' to total float.

Final Answer:
None of these