Please submit your responses in .pdf format file with your name and reg.no, in the file and the file name as well. 20 points Submission to be made online in the LMS by Thursday, 28th April 2022. 1. The R&D department is planning to bid on a large project for the development of a new communications system for commercial planes. The accompanying table shows the activities, times, and sequences required: ACTIVITY IMMEDIATE PREDECESSOR TIME (WEEKS) A B A A 3 2 4 D E F G A B CD DF D EGH H 1 a. Draw the network diagram. (2 points) b. What is the critical path? (2 points) 2. The following precedence diagram reflects three time estimates in weeks for each activity - for example, for Activity 1-2, the optimistic time estimate is 8 weeks, most likely time estimate is 8 weeks and the pessimistic time estimate is 8 weeks; similarly for Activity 3-8, the optimistic time estimate is 9 weeks, most likely time estimate is 10 weeks and the pessimistic time estimate is 12 weeks. Determine: a. All the paths in the project (1 point) b. The expected completion time for each path and its variance. Also determine the critical path. (Hint: calculate the expected time and variance for each activity. Then calculate the expected time and variance for all the identified paths by using the respective activity expected times and variances) (3 points) C. The probability that the project will require more than 49 weeks. (2 points) d. The probability that the project can be completed in 46 weeks or less. (2 points) 9-10-12 5-7-10 11-12-13 8-10-14 6 11 14-18-26 8-8-8 5-6-7 999 13-13-13 10.5-13-15.5 10 10-12-14 10-11-12 7-10-12 (How to read the activity times: for Activity 1-2, the optimistic time estimate is 8 weeks, most likely time estimate is 8 weeks and the pessimistic time estimate is 8 weeks; similarly for Activity 3-8, the optimistic time estimate is 9 weeks, most likely time estimate is 10 weeks and the pessimistic time estimate is 12 weeks.) 3. A project manager has compiled a list of major activities that will be required to install a computer information system in her firm. The list includes estimated completion times for activities and precedence relationships. a) Construct a network diagram. You can use either AOA or AON. (1 point) b) Calculate the expected time and variances for all the activities. (2 points) c) Identify all the paths (including path durations and path variances) and find the critical path (1 point) d) If the project is finished within 26 weeks of its start, the project manager will receive a bonus of $1,000; and if the project is finished within 27 weeks of its start, the bonus will be $500. Find the probability of each bonus. (4 points) How to read the time estimates in the table? - the time estimates are given in the following order: optimistic time - most likely time - pessimistic time Immediate Predecessor Activity Estimated Times (weeks) A D A D E I WILO 2-4-6 6-8-10 7-9-12 2-3-5 3-4-8 5-7-9 H E F G F OZ30TL - I - LUEZ 2-2-3 2-3-6 3-4-5 4-5-8 5-8-12 1-1-1 6-7-11 8-9-13 M End H, G, K, O