1. Consider the project network below. For each activity, you are given the estimates of a, b, and m in the table below. Deterrnine I. Determine the critical path for this network. Hint: duration of each activity (i) is the expected value E(Tij). II. Find the early event time ET(i) and late event time Lt(i) for each node i III. Find the probability that the project is completed within 40 days. Set up the LP that could be used to find the critical path and solve using Lingo. IV. Activity a b m (1.2). 4 8 6 (1,3) 2 8 4 (2,4) 1 7 3 (3,4) 6 12 9 (3,5). 1 5 15 10 (3,6) 17 18 12 (4,7) 5 12 9 (5,7) 1 3 2 (6,8) 2 16 3 (7,9) 10 2015 (8,9) 6 119