Consider the project with the listed activities. Normal durations and costs, as well as crash durations and costs are listed for each activity. Precedence relationships are implicitly given by the activity names (e.g., activity (1,2) is represented as an arc from node 1 to node 2). Crash Crash Normal Normal

Activity Time Cost Time Cost

(1, 2) 5 $41,000 8 $29,000

(1, 3) 2 $18,000 3 $10,000

(2, 4) 10 $50,000 12 $46,000

(2, 5) 4 $26,000 6 $20,000

(3, 5) 9 $18,000 11 $15,000

(4, 6) 4 $22,000 5 $20,000

(5, 6) 4 $13,000 4 $13,000

(5, 7) 8 $30,000 10 $25,000

(6, 8) 3 $15,000 5 $10,000

(7, 8) 4 $10,000 5 $7,000

*Times are in weeks

(a) Assuming that all activities are completed according to their normal durations, how long will it take to complete the project?

(b) Suppose that you wanted to shorten the duration of the project by 3 weeks. Which activities would you shorten, and by how much? What additional cost would you incur by doing this?