Problem 3) (20 pts) You have been given a small project to manage that your boss feels is important. Six tasks have been identified that define the project; the expected duration and precedence relationships between these tasks are indicated in the table below. Assume that the project begins at time 0. Duration Immediate Task (wks) Predecessor(s) Start A Start B Start C 10 Start D 5 A, B E C, D D END E, F a) Assuming that all precedence relationships are Finish-to-Start, use the Critical Path Method (CPM) (e.g., forward pass, backward pass) to find the early start times, early finish times, late start times, late finish times, total slacks and free slacks for each task. Which tasks are critical? b) Formulate a linear programming (i.e., Solver) model for finding the critical path. Using your Solver model, define the objective function so that all task occurrence times equal their earliest starting times in your solution. Change your objective function so that the task occurrence times equal their latest starting times. Using these early start and late start times, compute the early finish and late finish times, and total and free slack values for each task. Indicate which tasks lie on the critical path. Compare your solutions to the values you found in part (a). (You can use either a "Mark" model or a "Gary" model....or both.)