Problem 1 A project manager of a National forest is about to undertake a reforestation project in a burned-out area. Some of workers are very uncertain with respect to tie. 11 activities and their optimistic time (a), most likely time (m), and pessimistic time (b) are determined in days. Based on the assumption that the activity times follow a beta distribution, expected activity and variance of some activities are calculated and given in the table below. Activity Immediate Optimistic Predecessor Time(a) Most Likely Time (m) Pessimistic Time (b) Is Expected Time (days) Variance A 8 12 16 ?? ??? B 4 5 6 5 0.1111 C A 1 3 5 ?? ??? D A 2 4 12 ?? ??? E C 4 8 12 8 1.7778 F B,D 3 5 7- 5 0.4444 . G D,E,F 2 3 4 3 0.1111 H C 3 4 5 4 0.1111 I F 4 9 20 ?? 227 J EH 7 7 7 7 0 K G.J 1 4 7 4 1.0000 a) Draw the project network, determine ES.EE, LS,LF, and slack for each activity.. b) Find the critical path/s and mark on the network c) What is the expected project completion time? d) What s the probability that the project will be completed within 30 days? e) What is the probability that the project will be completed in more than 31 days but less than 36 days? f) What target project completion time would lead to a 98.5 probability of completion?