1. The following activities are part of a project to be scheduled using CPM:

Activity Immediate Predecessor Time (wks) A - 6 B A 3 C A 7 D C 2 E B,D 4 F D 3 G E,F 7 a. Draw the network b. What is the critical path? c. How many weeks will it take to complete the project? d. How much slack does activity B have? Solution b. A-C-D-E-G, also shown in the network above as the bold path. c. 26 weeks, 6+7+2+4+7. d. 6 weeks, 15-9. 2. For the project with the following information, a. Determine the critical path and the early completion time in weeks. b. Reduce the project completion time by three weeks. Assume a linear cost per week shortened, and show, step by step, how you arrived at your schedule. Solution a. A-B-D-G, 25 weeks, 5+10+6+4. b. First, reduce D (lowest cost activity on the critical path) by one week. This adds an additional critical path with activities C and E in it. Second, crash activity G by one week. Critical paths remain the same. Third, crash activity A by one week at a cost of $3,000, which is the least expensive. Summary of activities crashed: Step Activity Cost to crash Weeks reduced 1 D $1,000 1 2 G 2,000 1 3 A 3,000 1 Total cost $6,000