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?