1. Draw the network diagram. 2. Calculate the expected duration and variance of each activity. 3. Calculate the expected duration and variance of the critical path. 4. Calculate the probability that the project will be completed in less than 28 weeks.
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- The estimated times and immediate predecessorsfor the activities in a project at George Kyparis’s retinal scan-ning company are given in the following table. Assume thatthe activity times are independent. a) Calculate the expected time and variance for each activity.b) What is the expected completion time of the critical path?What is the expected completion time of the other path inthe network?c) What is the variance of the critical path? What is the vari-ance of the other path in the network?d) If the time to complete path A–C is normally distributed,what is the probability that this path will be finished in22 weeks or less?e) If the time to complete path B–D is normally distributed,what is the probability that this path will be finished in22 weeks or less?f) Explain why the probability that the critical path will befinished in 22 weeks or less is not necessarily the probabil-ity that the project will be finished in 22 weeks or less.Assume that we are considering the completion of a project one day earlier than the original plan. This project includes five activities and their normal and crash data are as follow: Activity Precedence Duration, Days (normal, crash) Cost (normal, crash) a - 3, 2 $40, $80 b a 2, 1 $20, $80 c a 2, 2 $20, $20 d a 4, 1 $30, $120 e b 3, 1 $10, $80 Note that partial crashing is always allowed. In this project, the critical path is a-b-e. Based on the information above, what is the best way to complete this project one day earlier? (0.5) How much does it cost? (0.5) Show all your work.I need a detailed explanation and assistance to solve the this problem: A company decides to plan a project, with activities, precedences and deterministic durations given in the following table: Activity i Duration (days) Immediate Predecessors A 32 none B 21 none C 30 none D 45 A E 26 A, B F 28 C G 20 E, F a) What method should be used? Using only one pseudo-activity, draw the project network, with arcs labeled by the activity name and duration. b) Compute and display in a table the earliest and latest starting and finishing times, as well as slack, for each activity, and identify the critical path(s). C) Draw a Gantt chart of the schedule, based on earliest starting times d) Which activities must be completed by day 60 to ensure that the project is not delayed?
- Consider again the project with the activity network shown in Figure 19.14.Activity A1 takes 4 days; A2, 2 days; A3, 10 days; A4, 4 days; A5, 2 days; A6, 3 days; A7,5 days; and A8, 2 days. Compute the earliest completion time of the project.Answer: 26 days.We start the project with A1 because it has no predecessor activity. A1 will take 4 days, sothe ECT for A1 is 4. Once A1 is complete, we can start on A2. A2 thus has an EST of 4. A2takes 2 days and hence has an ECT of 6.Following the completion of A2, we can initiate A3, A4, and A5. These activities thus canall have an EST of 6. We continue this process as shown in Table 19.13 and find that theearliest completion time is 26 days.Consider the following project network and activity times (in weeks): a. Identify the critical path. b. How much time will be needed to complete this project? c. Can activity D be delayed without delaying the entire project? If so, by how many weeks? d. Can activity C be delayed without delaying the entire project? If so, by how many weeks? e. What is the schedule for activity E?A project consists of five activities listed below. The project network is shown for the activities. The critical path is B-C-E and the expected completion time is 8. Optimistic Most Probable Pessimistic Activity Time (hr) Time (hr) Time (hr) A Floor sanding 3 4 5 B Paint mixing 0.5 1 1.5 C Ceiling painting 1 5.5 7 D Wall painting 1 2 9 E Floor buffing 1 2 3 What is the probability that the project can be completed within 9 hr.?
- A project's activities must be completed in the sequence indicated below. Activity Immediately Preceding Activity Duration in Weeks A - 3 B - 20 C - 15 D - 10 E - 5 F A 4 G D 3 H D, E 10 I F 3 J B 10 K G, H 7 L B, I 5 The project ends with the intersection of activities: C, J, K and L 1- Use CPM to construct (Draw) the project Network and find the critical path. 2- How long is the project expected to takeThe estimated times and immediate predecessors for the activities in a project a t George Kyparis's retinal scanning company are given in the following table. Assume that the activitytimes are independent. a) Calculate the expected time and variance for each activity.b) What is the expected completion time of the critical path?What is the expected completion time of the other path in the network?c) What is the variance of the critical path? Wha t is the variance of the other path in the network?d) If the time to complete path A-C is normally distributed, what is the probability that this path will be fini shed in 22 weeks or less?e) If the time to complete path B- D is normally distributed, what is the probability that this path will be finished in 22 weeks or less?f) Explain why the probability that the critical path will be finished in 22 weeks or…Three recent college graduates have formed a partnership and have opened an advertising firm.Their first project consists of activities listed in the following table.a. Draw the precedence diagram.b. What is the probability that the project can be completed in 24 days or less? In 21 days or less?c. Suppose it is now the end of the seventh day and that activities A and B have been completedwhile activity D is 50 percent completed. Time estimates for the completion of activity D are5, 6, and 7. Activities C and H are ready to begin. Determine the probability of finishing theproject by day 24 and the probability of finishing by day 21.TIME IN DAYSActivityImmediatePredecessor Optimistic Most Likely PessimisticA — 5 6 7B — 8 8 11C A 6 8 11D — 9 12 15E C 5 6 9F D 5 6 7G F 2 3 7H B 4 4 5I H 5 7 8End E, G, Id. The partners have decided that shortening the project by two days would be beneficial, as longas it doesn’t cost more than about $20,000. They have estimated the daily crashing costs for…
- 2. A small software development project at Krishna Dhir's firm has five major activities. The times (in days) are estimated and provided in the table below: Activity Immediate Predecessor a m b A − 2 5 8 B − 3 6 9 C A 4 7 10 D B 2 5 14 E C 3 3 3 Part 2 d) The probability that it will take more than 17 days to complete this projectbe is __ (keep two decimal places). e) The due date that yields a 98% chance of completion is ____ days (keep two decimal places).Which project management approach follows a deterministic approach and assumes the activity duration is a known certainty? a) PERT b) CPM c) Network Diagram d) JIT e) ABCYou are provided with the following information for a project, with activity durations given in weeks: Activity Immediate Optimistic Most Likely Pessimistic Predecessor Time (a) Time (m) Time (b) A ____ 2 3 4 B ____ 2 4 6 C A 1 2 3 D B 3 6 9 E C, D 7 8 9 F D 4 7 10 G E 3 4 5 H E, F…