Question 5

5. (23 marks) The table below shows the activities, their immediate predecessors and activity time estimates (in days) of a project. Immediate Most Activity Optimistic Pessimistic Predecessor Probable A 3 11 B 4 6 8 C A 2 3 10 D B 5 8 17 E A. B 6 8 16 F C, E W 5 7 G C, D J 15 17 (a) Determine mean time and variance for each activity and complete the following table. Activity Mean Time Variance A B C D E F G (b) Construct a complete project network for the project (c) Define the random variable T = completion time of the project. Find the mean and the standard deviation of T. (d) What is the probability that the project is completed in 25 days? (e) Suppose the (mean) times of D, E, F and G can be each cut down to 7 days, 6 days, 4 days and 11 days respectively, with crash costs of $100, $120, $140 and $125 per day respectively. Formulate a linear program to minimize the project completion time at a budget of $4200