A project has the activity duration and cost information indicated in the table where all times are in weeks.What is the lowest total cost for completing this project in 40 days?
A)$242,667
B)$255,600
C)$263,333
D)$272,500

Question

A project has the activity duration and cost information indicated in the table where all times are in weeks.What is the lowest total cost for completing this project in 40 days? 
A)$242,667 
B)$255,600 
C)$263,333 
D)$272,500

Quizplus · Accepted Answer

To complete the project in 40 days, we need to find the critical path with the shortest duration, and this path should not exceed 40 days. From the given table, we can first identify the duration of each path by adding up the times for each activity.

Path 1: A-B-D-F = 5+6+8+5 = 24 weeks 
Path 2: A-B-D-G-H-F = 5+6+10+3+5 = 29 weeks 
Path 3: A-C-E-F = 4+4+8+5 = 21 weeks 
Path 4: A-C-E-G-H-F = 4+4+10+3+5 = 26 weeks

The critical path is Path 2 because it has the longest duration (29 weeks). Therefore, the total project duration is 29 weeks. Since we are given the activity cost information, we can calculate the total cost for each path by adding up the costs for each activity on that path.

Path 1: $60,000+$50,000+$75,000+$35,000 = $220,000 
Path 2: $60,000+$50,000+$100,000+$60,000+$35,000 = $305,000 
Path 3: $40,000+$30,000+$80,000+$35,000 = $185,000 
Path 4: $40,000+$30,000+$100,000+$60,000+$35,000 = $265,000

Since we want to complete the project in 40 days, we have to shorten Path 2. We can shorten Path 2 by crashing activity G and activity H. By crashing an activity, we can reduce its duration and increase its cost. The table below shows the new durations and costs for each activity after crashing.

Activity G: 2 weeks -> 1 week, cost increases from $10,000 to $20,000 
Activity H: 3 weeks -> 2 weeks, cost increases from $15,000 to $25,000

The new durations and costs for each path are:

Path 1: 24 weeks 
Path 2: 5+6+10+1+2+5 = 29 weeks, cost increases from $305,000 to $335,000 
Path 3: 21 weeks 
Path 4: 26 weeks

The critical path is still Path 2 with a duration of 29 weeks. The total cost for completing the project in 29 weeks is $335,000. This is the lowest total cost for completing the project in 40 days (or 8 weeks). Therefore, the best choice is B.

A Project Has the Activity Duration and Cost Information Indicated