Activity 7.6 - Module Problems Complete the following problems and submit the results in either a Microsoft Word document or a Microsoft Excel spreadsheet. If you choose to use an Excel spreadsheet, place each problem on a separate sheet and label the tab with problem number. Save your document with a descriptive file name, including the assignment and your name. Chapter 11: 7-1 Jean Walker is making plans for spring break at the beaches in Florida. In applying techniques she learned in her quantitative methods class, she has identified the activities that are necessary to prepare for her trip. The following table lists the activities and the immediate predecessors. Draw the network for this project. Activity A B C D E F G Immediate Predecessors A A B C,D A E,F Critical path is A-B-D-E-G, which is annotated by the red line. The following are the activity times for Jean Walkers activities. Find the earliest, latest, and slack times for each activity. Then find the critical path. Activity A B C D E F Time (in days) 3 7 6 2 5 8 Page 1 of 8 qattachments_a639e5c88f8e4cb3d341f51a301ad60591117a62 G 4 The earliest, latest and slack times are listed in the above table. 7-2 Tom Schriber, a director of personnel of Management Resources, Inc., is in the process of designing a program that its customers can use in the job-finding process. Some of the activities include preparing resums, writing letters, making appointments to see prospective employers, researching companies and industries, and so on. Some of the information on the activities is shown in the following table: Days Activity A B C D E F G H I J K L a. a m 8 8 3 9 6 9 7 14 10 6 4 2 b 10 10 3 20 8 10 10 15 11 8 7 4 Immediate Predecessors 12 14 4 34 11 14 14 18 13 11 8 8 A C B,D,E B,D,E F F G,H I,J G,H Construct a network for this problem. Page 2 of 8 qattachments_a639e5c88f8e4cb3d341f51a301ad60591117a62 b. Determine the expected time and variance for each activity. The expected time is listed in the activity time column and has a standard deviation of 4.48 and a total variance of 20.08. c. Determine ES, EF, LS, LF, and slack for each activity. Page 3 of 8 qattachments_a639e5c88f8e4cb3d341f51a301ad60591117a62 The ES, EF, LS, LF and Slack are listed above. Determine the critical path and project completion time. The critical path is annotated by the \"red line\" in the network graph found in part A above, which is A-D-F-H-J-K. The project completion time is found in the above table, 71.17 days. e. Determine the probability that the project will be finished in 70 days or less. d. f. Probability is 0.397 or 39.7%. Determine the probability that the project will be finished in 80 days or less. g. Probability is 0.976 or 97.6%. Determine the probability that the project will be finished in 90 days or less. Page 4 of 8 qattachments_a639e5c88f8e4cb3d341f51a301ad60591117a62 Probability is 1.000 or 100%. 7-3 The air pollution project discussed in the chapter has progressed over the past several weeks, and it is now the end of week 8. Lester Harky would like to know the value of the work completed, the amount of any cost overruns or underruns for the project, and the extent to which the project is ahead of or behind schedule by developing a table like Table 11.8. The revised cost figures are shown in the following table: Activity A B C D E F G H Percent of Completion 100 100 100 100 50 60 10 10 Actual Cost ($) 20,000 36,000 26,000 44,000 25,000 15,000 5,000 1,000 The value of the work completed is $181,600 with an underrun of $9,600. The % of completion column highlights what activities are completed, ahead, or behind. 7-4 The Scott Corey accounting firm is installing a new computer system. Several things must be done to make sure the system works properly before all the accounts are put into the new system. The following table provides information about this project. How long will it take to install the system? What is the critical path? Immediate Page 5 of 8 qattachments_a639e5c88f8e4cb3d341f51a301ad60591117a62 Activity A B C D E F G H Predecessor(s) A B A C D,E F,G Time (weeks) 3 4 6 3 5 2 5 5 The total time it will take is 18 weeks and the critical path is A-E-G-H. 7-5 The managing partner of the Scott Corey accounting firm has decided that the system must be up and running in 16 weeks. Consequently, information about crashing the project was put together and is shown in the following table: Activity A B C D Immediate Predecessor(s ) A B Normal Time (weeks) Crash Time (weeks) Normal Cost ($) Crash Cost ($) 3 4 6 3 2 3 4 1 8,000 9,000 12,000 15,000 9,300 10,000 15,000 15,500 Page 6 of 8 qattachments_a639e5c88f8e4cb3d341f51a301ad60591117a62 E F G H a. A C D,E F,G 5 2 5 5 3 1 3 3 5,000 7,500 9,000 5,000 8,700 9,000 11,400 8,000 If the project is to be finished in 16 weeks, which activity or activities should be crashed to do this at the least additional cost? What is the total cost of this? If the project is to be finished in 16 weeks, then activity G would have to be crashed by 2 days. The cumulative cost of this action is $2,400. b. List all the paths in this network. After the crashing in part (a) has been done, what is the time required for each path? If the project completion time must be reduced another week so that the total time is 15 weeks, which activity or activities should be crashed? Page 7 of 8 qattachments_a639e5c88f8e4cb3d341f51a301ad60591117a62 Graph above is the network before crashing. Path A-C-F-H will require 16 weeks. Path A-E-G-H will require 18 weeks and is the critical path. Path B-D-G-H will require 17 weeks. Graph above is the network after crashing. Both graphs have the same paths, with the exception of the time. Path A-C-F-H will require 10 weeks. Path A-E-G-H will require 11 weeks and is the critical path. Path B-D-G-H will require 10 weeks. If the project completion time must be reduced by another week to meet a 15 week goal, then activity A must be crashed by 1 day and activity G must be crashed by 2 days with a total cost of $3,700. Page 8 of 8 qattachments_a639e5c88f8e4cb3d341f51a301ad60591117a62