Question

A small project has 12 activities – N, P, Q, R, S, T, U, V, W, X, Y, and Z. The relationship among these activities and the duration of these activities are given in the table. 
 

The total float of the activity “V” (in weeks, in integer) is _______________

Hint:

The float of an activity in a project can be calculated by subtracting the duration of the path including that activity from the total project duration.

Answer 1

Correct Answer: 0

To calculate the total float for activity \( V \), we need to consider the critical path of the project. The critical path is the longest path through the project and determines the minimum project duration. Activities on the critical path have zero float. First, calculate the project duration by identifying the critical path: - \( N \to P \to R \to T \to X \to Z \) (duration: 2 + 5 + 4 + 8 + 5 + 3 = 27 weeks)
Now, calculate the float for \( V \): - \( V \) depends on \( U \), and \( U \) depends on \( R \) and \( S \).
- The float for \( V \) is the difference between the total duration of the project and the duration of the path that includes \( V \).
The float for \( V \) is: \[ \text{Float of V} = \text{Total Project Duration} - (\text{Duration of Path to V} + \text{Duration of V}). \] The path to \( V \) is \( N \to P \to R \to U \to V \), and its duration is: \[ \text{Duration} = 2 + 5 + 4 + 7 + 2 = 20 \, \text{weeks}. \] Thus, the float for \( V \) is: \[ \text{Float of V} = 27 - 20 = 0 \, \text{weeks}. \] Thus, the total float of the activity \( V \) is \( \boxed{0} \) weeks.