# PROBLEMS100. Consider the network pictured below.a. Enumerate all paths through this network.b. Calc

PROBLEMS100. Consider the network pictured below.a. Enumerate all paths through this network.b. Calculate the critical path for the network.c. What is the minimum duration of the project?d. How much slack exists at each activity?101. A network consists of the activities in the following list. Times are given in weeks.Activity Preceding Timea. Draw the network diagram.b. Calculate the ES, EF, LS, LF, and Slack for each activity.c. What is project completion time?102. The network below represents a project being analyzed by Critical Path Methods. Activitydurations are A=5, B=2, C=12, D=3, E=5, F=1, G=7, H=2, I=10, and J=6.a. What task must be on the critical path, regardless of activity durations?b. What is the duration of path A-B-E-H-J?c. What is the critical path of this network?d. What is the length of the critical path?e. What is slack time at activity H?f. What is the Late Finish of activity H?103. A network consists of the following list. Times are given in weeks.Activity Preceding Durationa. Draw the network diagram.b. Which activities form the critical path?c. How much slack exists at activities A and F?d. What is the duration of the critical path?(a) Network diagram104. A partially solved PERT problem is detailed in the table below. Times are given in weeks.Activity Preceding Optimistica. Calculate the expected time for each activity. Enter these values in the appropriate column inthe table above.b. Which activities form the critical path?c. What is the estimated time of the critical path?d. What are the project variance and the project standard deviation?e. What is the probability of completion of the project after week 40?(a) A=9.5 B=3 C=12 D=5.5 E=6 F=8 G=3 H=3 I=9 J=7 K=2.5(b) A-D-H-I-J-K; (c) 36.5; (d) 9.53, 3.09; (e) 0.13.(Project management techniques: PERT and CPM, moderate) {AACSB: AnalyticSkills} 57105. Consider the network described in the table below.a. Calculate the expected duration of each activity.b. Calculate the expected duration and variance of the critical path.c. Calculate the probability that the project will be completed in fewer than 30 time units.106. The network below represents a project being analyzed by Critical Path Methods. Activitydurations are indicated on the network.a. Identify the activities on the critical path.b. What is the duration of the critical path?c. Calculate the amount of slack time at activity H.d. If activity I were delayed by ten time units, what would be the impact on the project duration?(a) Critical activities are A-C-J-K; (b) The critical path is 26 time units; (c) Slack at H is 9units; (d) I has 11 units slack–a ten unit delay would have no impact on the project.107. Three activities are candidates for crashing on a CPM network. Activity details are in thetable below.Activity Normal Time Normal Cost Crash Duration Crash CostX 8 days $6,000 6 days $8,000Y 3 days $1,800 2 days $2,400Z 12 days $5,000 9 days $7,700a. What is the crash cost per unit time for each of the three activities?b. Which activity should be crashed first to cut one day from the project’s duration; how much isadded to project cost?c. Which activity should be the next activity crashed to cut a second day from the project’sduration; how much is added to project cost?108. Three activities are candidates for crashing on a CPM network. Activity details are in thetable below.Activity Normal Time Normal Cost Crash Duration Crash CostA 9 days $8,000 7 days $12,000B 5 days $2,000 3 days $10,000C 12 days $9,000 11 days $12,000a. What is the crash cost per unit time for activity A?b. What is the crash cost per unit time for activity B?c. Which activity should be crashed first to cut one day from the project’s duration; how much isadded to project cost?d. Which activity should be the next activity crashed to cut a second day from the project’sduration; how much is added to project cost?e. Assuming no other paths become critical, how much can this project be shortened at what totaladded cost?

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