3 The table lists the duration (in hours), immediate predecessors and number of workers required for each activity in a project.

\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
Activity & Duration & Immediate predecessors & Number of workers \\
\hline
$A$ & 6 & - & 2 \\
\hline
B & 5 & - & 4 \\
\hline
C & 4 & - & 1 \\
\hline
D & 1 & $A , B$ & 3 \\
\hline
E & 2 & $B$ & 2 \\
\hline
$F$ & 1 & $B , C$ & 2 \\
\hline
$G$ & 2 & D, E & 4 \\
\hline
$H$ & 3 & D, E, F & 3 \\
\hline
\end{tabular}
\end{center}

(i) Draw an activity network, using activity on arc, to represent the project. You should make your diagram quite large so that there is room for working.\\
(ii) Carry out a forward pass and a backward pass through the activity network, showing the early and late event times clearly at the vertices of your network.

State the minimum project completion time and list the critical activities.\\
(iii) Using graph paper, draw a resource histogram to show the number of workers required each hour. Each activity begins at its earliest possible start time. Once an activity has started it runs for its duration without a break.

A delay from the supplier means that the start of activity $F$ is delayed.\\
(iv) By how much could the start of activity $F$ be delayed without affecting the minimum project completion time?

Suppose that only six workers are available after the first four hours of the project.\\
(v) Explain carefully what delay this will cause on the completion of the project. What is the maximum possible delay on the start of activity $F$, compared with its earliest possible start time in part (iii), without affecting the new minimum project completion time? Justify your answer.

\hfill \mbox{\textit{OCR D2 2010 Q3 [15]}}