QUESTION #5: [10 Marks] McGee Carpet and Trim installs carpets in commercial offices. Andrea McGee has been concerned with the amount of time it took to complete several recent jobs. Some of her workers are very unreliable. A list of activities and their optimistic completion time, the most likely completion time, and the pessimistic completion time (all in days) for a new contract are given in the following table. Time (days) Most Probable m 3 Optimistic a 2 Activity A Pessimistic b 4 Immediate Predecessor(s) B 2 4 6 A 1 2 3 A D 1 3 5 B E 2 3 4 D F 1 4 7 B, C G 2 2 2 B, C H 2 5 8 F I 1 3 5 F, G J 2 3 4 HI (a) Draw the AON (activity on node) network for this project (add a Start node and/or an End/Finish node to your network as required). Note: you can draw the network by hand, take a scan/picture/photo of the graph, then copy and paste the picture into your Word document for grading purposes.) (3 marks) (b) Determine the expected completion time and the standard deviation for each activity. Summarize your calculations in the form of a table with appropriate headings. (1 mark) (c) Using the expected completion times calculated in part (b), find the earliest start times, earliest finish times, latest start times, latest finish times, and slack for each activity. Summarize your calculations in the form of a table showing the activity schedule for an example of activity schedule, see Slide 32 of Lesson 2A or Table 3.3 page 74 in the Textbook 3Ce.) (2.5 marks) (d) Determine the expected) project completion time and the critical path for the project. (1 mark) (e) What is the probability that McGee Carpet and Trim will finish the project in 20 days or less? (1.5 marks) (1) How many days should be allowed to give a 95% probability of completing the project (1.e. critical path based expected completion times) on time? (1 mark) QUESTION #6: [10 Marks] Consider the project and activity network of QUESTION#5. The following are estimates of costs for completing each activity in crash time and normal time, where the times correspond to the optimistic time (shown in the table given in QUESTION#5 and expected time (computed in part (b) of QUESTION#5), respectively. Activity Crash Cost ($) 20 Normal Cost ($) 12 B 50 40 40 30 D 20 14 E 60 45 F 35 20 G 30 30 H 25 10 30 15 J 12 10 (a) Prepare a table showing the normal time, normal cost, crash time, crash cost, maximum crash days, and cost per crash day for each activity. (3 marks) (b) (3 marks) Using the results of part (a), what would be the minimum cost of the project if it were to be completed in: 1) 19 days? 2) 18 days? : 3) 17 days? () (4 marks) We want to formulate part of a linear programming (LP) model that will assess the additional cost of reducing the completion time to 9 days. Recall that the decision variables in the LP model are defined as: Xi= the finish time for activity i and yi = the amount of time activity i is crashed, i = A, B, C, ... J. Use the results of part (a) and the given precedence relationships among the activities of this project to answer the following questions: 1) State the objective function of the LP model. 2) Write the constraint(s) corresponding to the finish time of activity D. 3) Write the constraint(s) corresponding to the finish time of activity F. 4) Write the constraint(s) to ensure that the project will be completed in 9 days or less