Jetta Engineering Company (JEC) receives a contract to shift and upgrade the Zee manufacturing plant to its new location, which is scheduled to start in July. They are concerned with the completion time as some of their workers are highly unreliable. List of activities and their optimistic, pessimistic, and most likely completion time estimates (in weeks) assuming that each activity time follows an independent Beta distribution are developed. Partial data regarding this project is given in the following table. Activity A B C D Immediate Predecessor(s) None A None A, C B, D D D E. G 4 F.H ?? E 7 G 9 J 5 a) Draw the project network. Calculate the early and late times, and the corresponding slack times for each activity. Using these slack times determine the critical path(s) and mark it (them) on the project network. What is the expected completion time of the project? b) What is the probability that JEC will take more than 37 weeks to complete the project? c) What is the probability that JEC will complete the project in more than 32 weeks but less than 40 weeks? E F H G T J Optimistic Most Likely 6 K 3 2 4 4 4 lin 7 6 Pessimistic E(t) 5 21 65 10 14 6 0 8 9 9 7 5 ?? 9.0000 4.0000 2.2500 1.3611 1.7778 77 1.5625 ?? 1.0000 2.7778 6.2500 0.1111 d) If JEC wants a 87.75% probability of completing the project on time, how early from the due date should they begin working on the project?