1. Jean Walker is making plans for spring break at the beaches in Florida. In applying techniques she learned in her quantitative methods class, she has identified the activities that are necessary to prepare for her trip. The following table lists the activities and the immediate predecessors. Draw the network for this project.
Activity Immediate Predecessor
E C, D
G E, F
2. 2. The following are the activity times for the project in the problem above. Find the earliest, latest, and slack times for each activity. Then find the critical path.
Activity Time (Days)
3. Tom Schriber, a director of personnel of Management Resources, Inc., is in the process of designing a program that its customers can use in the job-finding process. Some of the activities include preparing resumes, writing letters, making appointments to see prospective employers, researching companies and industries, and so on. Some of the information on the activities is shown the following table:
Activity a m b Prodecessors
A 8 10 12 –
B 6 7 9 –
C 3 3 4 –
D 10 20 30 A
E 6 7 8 C
F 9 10 11 B, D, E
G 6 7 10 B, D, E
H 14 15 16 F
I 10 11 13 F
J 6 7 8 G, H
K 4 7 8 I, J
L 1 2 4 G, H
a. Construct a network for this problem.
b. Determine the expected time and variance for each activity.
C. Determine ES, EF, LS, LF, and slack for each activity.
d. Determine the critical path and project completion time.
e. Determine the probability that the project will be finished in 70 days or less.
f. Determine the probability that the project will be finished in 80 days or less.
g. Determine the probability that the project will be finished in 90 days or less.
4. Bowman Builders manufactures steel storage sheds for commercial use. Joe Bowman, president of Bowman Builders, is contemplating producing sheds for home use. The activities necessary to build an experimental model and related data are given in the accompanying table.
a. What is the project completion date?
b. Formulate an LP problem to crash this project to 10 weeks. Normal Crash Normal Crash Activity Time Time Cost Cost Immediate Predecessors
A 3 2 $1,000 $1,600 –
B 2 1 $2,000 $2,700 –
C 1 1 300 300 –
D 7 3 1,300 1,600 A
E 6 3 850 1,000 B
F 2 1 4,000 5,000 C
G 4 2 1,500 2,000 D, E