4 Henry is planning a surprise party for Lucinda. He has left the arrangements until the last moment, so he will hold the party at their home. The table below lists the activities involved, the expected durations, the immediate predecessors and the number of people needed for each activity. Henry has some friends who will help him, so more than one activity can be done at a time.

\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
Activity & Duration (hours) & Preceded by & Number of people \\
\hline
A: Telephone other friends & 2 & - & 3 \\
\hline
$B$ : Buy food & 1 & A & 2 \\
\hline
C: Prepare food & 4 & B & 5 \\
\hline
D: Make decorations & 3 & A & 3 \\
\hline
$E$ : Put up decorations & 1 & D & 3 \\
\hline
$F$ : Guests arrive & 1 & C, E & 1 \\
\hline
\end{tabular}
\end{center}

(i) Draw an activity network to represent these activities and the precedences. Carry out forward and reverse passes to determine the minimum completion time and the critical activities. If Lucinda is expected home at 7.00 p.m., what is the latest time that Henry or his friends can begin telephoning the other friends?\\
(ii) Draw a resource histogram showing time on the horizontal axis and number of people needed on the vertical axis, assuming that each activity starts at its earliest possible start time. What is the maximum number of people needed at any one time?\\
(iii) Now suppose that Henry's friends can start buying the food and making the decorations as soon as the telephoning begins. Construct a timetable, with a column for 'time' and a column for each person, showing who should do which activity when, in order than the party can be organised in the minimum time using a total of only six people (Henry and five friends). When should the telephoning begin with this schedule?

\hfill \mbox{\textit{OCR D2  Q4 [13]}}