Martha Design Agency (MDA) needs to redesign the Stedman Lecture rooms, which is scheduled to start in June. They are concerned with the completion time. Some of their workers are highly unreliable. List of activities and for each activity an optimistic completion time (a), a most likely completion time (m), and a pessimistic completion time (b) are determined. Based on the assumption that the activity times follow a beta distribution, the expected activity time and the variance of each activity are calculated for you and are given in the table below: Activity Immediate Predecessor (s) Expected time (days) Activity Variance A None 6 1.8906 B A 3 0.1111 C None 3 0.2500 D A,C 1.3611 E D. G 0.4444 F B, D 2.7778 G None 1.5625 G 0.5625 H F 5 0.250 1 E,F.H 5 J 0.5017 2 0.1111 K 1, J J 3 0.4444 L a) Construct a network diagram and determine ES, EF, LS, LF and slack for each activity. Mark/indicate critical path on the network. b) What is the probability that MDA will take more than 21 days to complete the project? c) What is the probability that MDA will take more than 23 days but less than 29 days to complete the project? the d) If MDA wants to complete the project with a 91.50% assurance, how many days early due date should they start the project? You can leave your answer in decimals.