Jacksonville National Bank is scheduling the installation of a new e-banking system. There are several activities required to achieve this project successfully. The table below lists each of these activities, their precedence relationships, and activity time estimates. Time Estimates (weeks) Part I a. Activity Description Predecessor a m b a Position recruiting 5 11 17 b System development 9 12 15 C System training a 4 7 16 d Equipment training a 5 11 23 e Manual system test b, c 1 3 5 f Preliminary system changeover b, c 5 9 13 g Computer-personnel interface d, e 2 5 8 h Equipment modification d, e 2 3 10 i Equipment testing b, c 1 2 3 System debugging and installation f, g 3 3 3 k Equipment changeover g.i 3 5 7 Calculate the expected activity time and variance for each activity. Show your calculations. b. Draw the network diagram for this project. Show your calculations. C. Use the critical path method (showing the forward and backward pass) to determine the earliest and latest activity times and the expected project completion time. Show your work. d. Set up the linear program in Excel and use Solver to confirm your expected completion time in Part c. e. Calculate the project variance and standard deviation. Show your calculations. f. What the probability that the project will be completed in 40 weeks or less? Show your calculations. Part II The following table provides the crash data for the project. The chart shows the maximum number of weeks each activity can be crashed, the normal cost associated with each activity, and the cost of crashing each activity 1 week. Assume the expected activity times calculated in Part I(a) are the "Normal" activity times. Maximum number of Normal activity Crash cost per week Activity weeks to crash cost ($) ($) a 4 5000 1000 b 3 8500 2000 C 4 2500 500 d 4 4000 625 e 0 0 0 f 6 1500 200 g 1 2000 750 h 0 0 0 i 0 0 0 j 0 k 2 0 4000 0 1750 a. On a separate worksheet, set up your linear program in Excel and use Excel Solver to determine how soon the project can be completed if it was crashed the maximum amount. b. How much it would cost the bank to crash the maximum amount?