Question

The activity details for a small project are given in the Table. 

\[ \begin{array}{|c|c|c|} \hline \text{Activity} & \text{Duration (days)} & \text{Depends on} \\ \hline A & 6 & - \\ B & 10 & A  \\ C & 14 & A \\ D & 8 & B \\ E & 12 & C \\ F & 8 & C \\ G & 16 & D, E \\ H & 8 & F, G \\ K & 2 & B \\ L & 5 & G, K \\ \hline \end{array} \] 

The total time (in days, in integer) for project completion is \(\underline{\hspace{2cm}}\). 
 

Hint:

To find the total time for project completion, identify the critical path by calculating the longest sequence of activities, considering their dependencies and durations.

Answer 1

Correct Answer: 56

To calculate the total time for project completion, we need to find the critical path, which determines the longest time for the project. The critical path is the longest sequence of activities from start to finish, considering dependencies and durations. We start with the initial activities: - \( A \) takes 6 days, so \( B \) and \( C \) can start after that. - \( B \) takes 10 days, so \( D \) can start after 10 days. - \( C \) takes 14 days, so \( E \) and \( F \) can start after that. - \( D \) and \( E \) take 8 and 12 days, respectively, so \( G \) can start after 16 days. From this, we can determine the total duration of the project: - The longest sequence of activities is \( A \to B \to D \to G \to H \), which takes \( 6 + 10 + 8 + 16 + 8 = 48 \) days. - Adding the durations of the remaining activities, we find the total project duration is \( \boxed{56} \, \text{days} \).