Three recent college graduates have formed a partnership and have opened an advertising firm.

Their first project consists of activities listed in the following table.

a. Draw the precedence diagram.

b. What is the probability that the project can be completed in 24 days or less? In 21 days or less?

c. Suppose it is now the end of the seventh day and that activities A and B have been completed, while activity D is 50 percent completed. Time estimates for the completion of activity D are 5, 6, and 7. Activities C and H are ready to begin. Determine the probability of finishing the project by day 24 and the probability of finishing by day 21.

TIME IN DAYS Activity Immediate Predecessor Optimistic Most Likely Pessimistic A — 5 6 7 B — 8 8 11 C A 6 8 11 D — 9 12 15 E C 5 6 9 F D 5 6 7 G F 2 3 7 H B 4 4 5 I H 5 7 8 End E, G, I

d. The partners have decided that shortening the project by two days would be beneficial, as long as it doesn’t cost more than about $20,000. They have estimated the daily crashing costs for each activity in thousands, as shown in the following table. Which activities should be crashed, and what further analysis would they probably want to do?
Activity First Crash Second Crash C $8 $10 D 10 11 E 9 10 F 7 9 G 8 9 H 7 8 I 6 8 LO.1