Question 1 (40 marks) A construction project is modelled by the set of activities illustrated in the table below. Code Predecessor's A Time (Days) 3 5 10 B A B D 12 E 6 F OO AO E G 12 10 17 No Activity 1 Preparatory Works 2 Excavation Works 3 Foundation Works 4 Column Structure Works 5 Sloof Works 6 Wall and Frame Works 7 Roof Trust Works 8 Roof (Ceilings and Tiles) Works 9 Sanitary Works and Electrical Installations 10 Plaster Works 11 Floor Works 12 Installation Works (Lamps, Glass, Doors, Windows, Switches, Outlets, Locks, Sanitation) 13 Painting Works 14 Fencing Works 15 Complementary Works H D G F, H F. H I J 20 25 18 15 K L I F M N 30 10 J. K L M, N O 6 Duration Activity Te S To Tm Tp A 2 3 4 3 5 B 3 5 8 Legend 10 10 15 11 D 10 12 17 13 To: Optimistic time E 5 6 8 6 Tm: mean time F 12 12 18 13 Tp: pessimistic time G 8 10 13 10 17 15 17 V: Variance H I 0.11 0.33 0.25 0,5 0,69 0.83 1.36 1.17 0.25 0,5 1 1 0.69 0.83 0,69 0.83 0,69 0.83 2,78 1.67 1,78 1.33 0,69 0.83 2.78 1.67 0.69 0,028 0,17 S: Standard deviation 20 25 35 23 20 25 15 20 25 21 27 J K Time estimates are in days 18 18 L 15 18 15 13 30 40 32 M N O 30 10 6 14 11 9 6 0.83 7 6 (a) Distinguish between the CPM and PERT explaining the appropriateness of each. [6 marks] (b) Compare the time estimates for the project completion under CPM and PERT. Use the two time estimates to work out the probability of project completion. [30 marks] (c) Explain the implications of reducing project completion time? [4 marks]