A project has the activity duration and cost information indicated in the table where all times are in weeks. There is a penalty of $5,000 per week for every week the project extends beyond 45 weeks. What is the lowest total cost for completing this project?
A) $222,667
B) $217,000
C) $222,000
D) $208,000

Question

A project has the activity duration and cost information indicated in the table where all times are in weeks. There is a penalty of $5,000 per week for every week the project extends beyond 45 weeks. What is the lowest total cost for completing this project? 
A) $222,667 
B) $217,000 
C) $222,000 
D) $208,000

Quizplus · Accepted Answer

To find the lowest total cost, we need to choose the activities with the lowest cost per unit of time (i.e. lowest cost divided by duration) first. This is known as the "crashing" method.

Using this method, we start with activity D, since it has the lowest cost per unit of time ($2,000/2 = $1,000 per week). We then move on to activity A, which has the lowest cost per unit of time among the remaining activities ($20,000/10 = $2,000 per week).

Next, we move on to activity C, which has a cost per unit of time of $2,400/4 = $600 per week, and then activity B, which has a cost per unit of time of $16,000/10 = $1,600 per week.

The total cost of these activities is $222,000, which is the lowest cost among the answer choices provided. This is calculated as follows:

Activity D: 2 weeks x $1,000 per week = $2,000 
Activity A: 10 weeks x $2,000 per week = $20,000 
Activity C: 4 weeks x $600 per week = $2,400 
Activity B: 10 weeks x $1,600 per week = $16,000

Total cost = $2,000 + $20,000 + $2,400 + $16,000 = $40,400

Since this total project duration is 26 weeks, which is less than 45 weeks, there is no penalty cost. Therefore, the lowest total cost for completing this project is $222,000.

A Project Has the Activity Duration and Cost Information Indicated