Chapter 3Project MANAGEMENTProblems:1. The following activities are part of a project to be scheduled using CPM:

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?

2. Schedule the following activities using CPM:

a. Draw the network path.b. What is the critical path?c. How many weeks will it take to complete the project?d. Which activities have slack, and how much?3. The R&D department is planning to bid on a large project for the development of a new communications system for commercial planes. The accompanying table shows the activities, times, and sequences required:

a. Draw the network diagram. b. What is the critical path?c. Suppose you want to shorten the completion time as much as possible, and you have the option of shortening any or all of B, C, D, and G each one week. Which would you shorten?d. What is the new critical path and earliest completion time?

4. A construction project is broken down into the following 10 activities:

a. Draw the network diagram.b. Find the critical path. c. If activities 1 and 10 cannot be shortened, but activities 2 and 9 can be shortened to a minimum of one week each at a cost of $10,000 per week, which activities would you shorten to cut the project by four weeks?5. The following represents a project that should be scheduled using CPM:

a. Draw the network.b. What is the critical path?c. What is the expected project completion time?d. What is the probability of completing this project within 16 days?

6. There is an 82 percent chance the project below can be completed in X weeks or less. What is X?

7. Here is a CPM network with activity times in weeks:

a. Determine the critical path. b. How many weeks will the project take to complete?26 weeksc. Suppose F could be shortened by two weeks and B by one week. How would this affect the completion date?

8. The following table represents a plan for a project:

a. Construct the appropriate network diagram. b. Indicate the critical path. c. What is the expected completion time for the project?d. You can accomplish any one of the following at an additional cost of $1,500:(1)Reduce job 5 by two days.(2) Reduce job 3 by two days.(3) Reduce job 7 by two days. If you save $1,000 for each day that the earliest completion time is reduced, which action, if any, would you choose?e. What is the possibility that the project will take more than 30 days to complete?

9. Here is a network with the activity times shown in days:

a. Find the critical path. b. The following table shows the normal times and the crash times, along with the associated costs for each activity.

If the project is to be shortened by four days, show which activities, in order of reduction would be shortened and the resulting cost.