Consider the project with the following dependency matrix.

a) Draw an activity network diagram and compute the earliest completion time of the project using EST/ECT. b) Draw a Gantt chart for this project including slack times (Optional: utilize commercial software if possible).

\begin{tabular}{|c|c|c|} \hline Activity & Predecessor & Activity Time (Days) \\ \hline 1 & & 2 \\ \hline 2 & 1 & 5 \\ \hline 3 & 2 & 7 \\ \hline 4 & 2 & 3 \\ \hline 5 & 2 & 4 \\ \hline 6 & 4,5 & 6 \\ \hline 7 & 3,6 & 3 \\ \hline 8 & 6,7 & 8 \\ \hline \end{tabular}