a m 1 2 QUESTION FOUR The time estimate (in weeks) for the activities of a PERT network are given below. Activity 1-2 1-3 1-4 2-5 3-5 4-6 5-6 1 B 7 7 8 1 14 8 15 4 2 1 5 5 6 2 2 3 (a) Draw the project network and identify all the paths through it. 4 marks (b) Determine the expected project length. 2 marks (c) Calculate the standard deviation and variance of the project length. 4 marks (d) What is the probability that the project will be complete: (1) at least 4 weeks earlier than expected time? 2 marks (2) no more that 4 weeks later than expected time? 2 marks (e) If the project due date is 19 weeks, what is the probability of not meeting the due date? 2 marks (1) The probability than the project will be completed on schedule if the scheduled completion time is 20 weeks. 2 marks (g) What should be the scheduled completion time for the probability of completion to be 2 marks 90%? QUESTION THREE The cost matrix giving selling costs per unit of a product by salesman A, B, C and Din Regions R1, R2, R3 and R4 is given below: (i) Assign one salesman to one region to minimize selling cost. 8 marks () If the selling price of the product is K200 per unit and variable cost excluding the selling cost given in the table is K100 per unit, find the assignment that would maximize the contribution 10 marks (IHI) What other conclusion can you make from the above? 2 marks A B C D R1 4 12 16 8 R2 20 28 32 24 R3 36 44 48 40 R4 52 60 64 56