Finding the critical path of a construction project

Question

Problem: A construction project is broken down into the following 10 activities:

Activity    Immediate Predecessor    Time (Weeks)
1    --         4
2    1          2
3    1          4
4    1          3
5    2, 3      5
6    3          6
7    4          2
8    5          3
9    6, 7      5
10  8, 9      7

a. Find the critical path.

b. If activities 1 and 10 can't be shortened, but activities 2 through 9 can be shortened to a minimum of one week each at a cost $10,000 per week, which activities would you shorten to cut the project by four weeks?