D1 January 2011 Q7

EdexcelOld spec16 marksCritical Path Analysis

7.

Figure 7: activity network on events 1 to 9: A (4) 1–2, B (6) 1–3, C (3) 2–3, D (7) 2–5, E (4) 2–4, F (3) 3–4, G (5) 3–6, H (2) 4–6, dummy 4–5, I (3) 5–7, dummy 6–7, J (9) 6–9, K (5) 7–8, L (3) 7–9, dummy 8–9
Figure 7

The network in Figure 7 shows the activities that need to be undertaken to complete a maintenance project. The activities are represented by the arcs. The number in brackets on each arc gives the time, in days, to complete the activity. The numbers in circles are the events.

Each activity requires one worker. The project is to be completed in the shortest possible time.

(a) Complete the precedence table for this network in the answer book. (3)
(b) Explain why each of the following is necessary.
(i) The dummy from event 6 to event 7.
(ii) The dummy from event 8 to event 9.
(3)
(c) Complete Diagram 2 in the answer book to show the early and the late event times. (4)
(d) State the critical activities. (2)
(e) Calculate the total float on activity K. You must make the numbers used in your calculation clear. (2)
(f) Calculate a lower bound for the number of workers needed to complete the project in the minimum time. (2)
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