D1 January 2006 Q5
5.
The network in Figure 5 shows the activities involved in a process. The activities are represented by the arcs. The number in brackets on each arc gives the time, in days, taken to complete the activity.
(a) Calculate the early time and late time for each event, showing them on the diagram in the answer book. (4)
(b) Determine the critical activities and the length of the critical path. (2)
(c) On the grid in the answer book, draw a cascade (Gantt) chart for the process. (4)
Each activity requires only one worker, and workers may not share an activity.
(d) Use your cascade chart to determine the minimum numbers of workers required to complete the process in the minimum time. Explain your reasoning clearly. (2)
(e) Schedule the activities, using the number of workers you found in part (d), so that the process is completed in the shortest time. (3)
| Scheme | Marks |
|---|---|
 | M1 A1 M1 A1 |
| (4) |
| Scheme | Marks |
|---|---|
| \(A\ C\ I\ M\) length 26 | B1 B1ft |
| (2) |
| Scheme | Marks |
|---|---|
 | M1 A3,2ft,1ft,0 |
| (4) |
| Scheme | Marks |
|---|---|
| 5 workers needed e.g. ref to 13–14 when \(C, F, H, J\) and \(K\) must be taking place e.g. ref to 18–19 when \(I\ F\ J\ K\ L\) must be taking place | B2,1,0 |
| (2) |
| Scheme | Marks |
|---|---|
e.g. | M1 A2,1,0 |
| (3) | |
| (15 marks) |