$2.$ Consider the following project with activities A through H $.$

a$.$ Draw the precedence diagram for this project.

b$.$ Using the critical path method, determine the earliest start, earliest finish, latest start, and latest finish times for each activity. Also calculate the slack for each activity.

c$.$ What is the minimum amount of time needed to complete the renovation project? Also, what are the critical activities and the critical path$($s$)$ of the project?

d$.$ Suppose now that we are given the following crashing information. For each week that we are able to reduce the project completion time, we are paid an extra $\backslash (\backslash$$ $800\backslash ).$ Using the greedy method learned in class, crash the project for as many weeks as it is profitable to do so$.$ Clearly show which activities you will crash for each week, the cost of crashing for each week, and all of the critical paths at the end of each week. If it becomes no longer profitable to crash the project, then clearly explain why.