Question

Painting is one of the activities in a construction project. For the painting activity that takes 6 days, both the total float and the free float are zero.
Which ONE of the following is TRUE for the painting activity?

• A. Painting is a dummy activity.
• B. Painting is a non-critical activity.
• C. The start of painting activity can be delayed without causing delay in completion of the construction project.
• D. The start of painting activity cannot be delayed without causing delay in completion of the construction project.

Hint:

Zero total float means an activity lies on the critical path, so recall what that implies about delaying its start.

Answer 1

The Correct Option is D

Step 1: Two Kinds of Float, and What Zero Means for Both:
Total float measures slack against the whole project's finish date, while free float measures slack only against the early start of the very next activity in the same chain.
When BOTH of these are zero at once for painting, it tells us there is no cushion anywhere, not against the immediate next activity and not against the far off project completion date either.

Step 2: Ruling Out the Dummy Activity Idea:
A dummy activity exists purely on paper to enforce a precedence link and always carries zero time, written as $duration = 0$.
Painting has a real duration of $6$ days doing actual work, so by definition it cannot be a dummy activity, this removes option (A) right away.

Step 3: Using the Critical Path Test:
The standard test for whether an activity lies on the critical path is simply $TF = 0$.
Painting satisfies $TF = 0$, so it must lie on the critical path, meaning it is critical, not non critical, this removes option (B).

Step 4: Testing the Delay Claim:
If an activity truly had spare time to shift its start, its total float would be a positive number, not zero.
Because painting shows $TF = 0$, there is exactly zero days of leeway, so pushing its start even by one day forces the project's completion date to move by that same one day.
This directly rules out option (C), which wrongly claims a delay is harmless, and confirms option (D), which correctly states a delay is not harmless.

Final Answer:
Zero float on both counts means painting sits on the critical path and any delay to its start delays the whole project.
\[ \boxed{\text{The start of painting cannot be delayed without delaying the project}} \]