Question

A project network consists of the following activities

\[\begin{array}{|c|c|c|} \hline \textbf{Activity} & \textbf{Immediate Predecessors} & \textbf{Duration (days)} \\ \hline \text{A} & \text{--} & 3 \\ \hline \text{B} & \text{--} & 4 \\ \hline \text{C} & \text{A, B} & 5 \\ \hline \text{D} & \text{B} & 6 \\ \hline \text{E} & \text{D} & 7 \\ \hline \text{F} & \text{C, E} & 8 \\ \hline \text{G} & \text{D} & 9 \\ \hline \text{H} & \text{F, G} & X \\ \hline \end{array}\]
 

If the project completion time is 30 days, then the value of \( X \), in days, is \(\underline{\hspace{2cm}}\) (in integer).

Hint:

When determining project completion time, consider the critical path which involves summing up the durations of the longest sequence of dependent activities.

Answer 1

Correct Answer: 5

To solve this, we need to calculate the project duration by considering the longest path in the network (critical path). We will calculate the early and late start times for each activity. Start with activities A and B. Their durations are given directly as 3 and 4 days, respectively. Then, calculate the start times for the next activities based on the dependencies. Using backward calculation for the final completion time of 30 days: - Activity H depends on F and G, and the project completion time is 30 days. Thus, \( X \) must satisfy the equation for the total duration from the start to the finish: \[ 3 + 4 + 5 + 6 + 7 + 8 + 9 + X = 30 \implies X = 5 \] Thus, the value of \( X \) is: \[ \boxed{5} \]