A project has been subdivided into five activities. Their immediate predecessors & the estimated activity durations (optimistic, most likely, & pessimistic) are shown in the table below. + Activity Immediate Predecessor B B D E Estimated duration (in days) 5, 5, 11 1,5,9 3,4,5 2, 2, 2 1.3.5 B 4, C BD (a) Draw the network & determine the critical path(s) by using the usual forward & backward recursions. (b) Determine the variances of all activities on the critical path. (c) Calculate the probability that the project duration is between 15 & 19 days. Show all work. (d) Suppose that a contractor has signed to finish the project within 14 days. In case the project is not finished within that time, there is a penalty of $1,000. What (if any) is the expected penalty the contractor has to pay