4. The following list gives the names of some students who have represented Britain in the International Mathematics Olympiad. Roper ( \(R\) ), Palmer ( \(P\) ), Boase ( \(B\) ), Young ( \(Y\) ), Thomas ( \(T\) ), Kenney ( \(K\) ), Morris ( \(M\) ), Halliwell ( \(H\) ), Wicker ( \(W\) ), Garesalingam ( \(G\) ).

1. Use the quick sort algorithm to sort the names above into alphabetical order.
2. Use the binary search algorithm to locate the name Kenney.
   (4)
   \includegraphics[max width=\textwidth, alt={}, center]{9ca3e12a-63fa-49c9-91fc-eedfb024417a-4_488_1573_392_239} The network in Fig. 3 shows the activities involved in the process of producing a perfume. The activities are represented by the arcs. The number in brackets on each arc gives the time, in hours, taken to complete the activity.
3. Calculate the early time and the late time for each event, showing them on Diagram 1 in the answer booklet.
4. Hence determine the critical activities.
5. Calculate the total float time for \(D\). Each activity requires only one person.
6. Find a lower bound for the number of workers needed to complete the process in the minimum time. Given that there are only three workers available, and that workers may not share an activity,
7. schedule the activities so that the process is completed in the shortest time. Use the time line in the answer booklet. State the new shortest time.
   (5)