PERT and Activity Crashing

A project is characterized by activities A through F. The predecessor activities and the times required, and costs for both a regular and crash program for each activity are shown in the attached table.

a. Using only the time for the regular program activities, draw a PERT network for this problem. What is the critical path? How long will it take to complete the total project?

I believe the critical path is A, B, E and it will take 9 days to complete the project but I am not sure this is correct.

b. What is the cost of the project as given in a. (I believe the cost is $32,000)
c. Find the time-cost trade-off points that are possible. What is the minimum time in which the project can be completed? What is the cost of this program?