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 35 days? $\begin{array}{|l|l|l|l|l|l}
& & \text { Normal } & \text { Normal } & & \
\text { Activity } & \text { Predecessor } & \text { Time } & \text { Cost } & \text { Crash Time } & \text { Crash Cost } \
\hline \mathbf{A} & -- & 3 & \$ 12,000 & 5 & \$ 22,000 \
\hline \mathrm{B} & \mathrm{A} & 12 & \$ 18,000 & 9 & \$ 32,000 \
\hline \mathrm{C} & \mathrm{A} & 15 & \$ 22,000 & 9 & \$ 62,000 \
\hline \mathrm{D} & \mathrm{B} & 3 & \$ 9,000 & & \$ 18,000 \
\hline \mathbb{E} & \mathrm{C} & 9 & \$ 15,000 & 5 & \$ 35,000 \
\hline \mathrm{F} & \mathbb{E} & 7 & \$ 5,000 & 5 & \$ 8,000 \
\hline \mathrm{G} & \mathrm{D} & 3 & \$ 13,000 & 6 & \$ 23,000 \
\hline \mathbb{H} & \mathrm{A} & 12 & \$ 20,000 & 8 & \$ 32,000 \
\hline \mathrm{J} & \mathbb{H} & 6 & \$ 45,000 & 4 & \$ 56,000 \
\hline
\end{array}$
A) $211,500
B) $197,500
C) $203,500
D) $194,500

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 35 days? $\begin{array}{|l|l|l|l|l|l} 
& & \text { Normal } & \text { Normal } & & \
\text { Activity } & \text { Predecessor } & \text { Time } & \text { Cost } & \text { Crash Time } & \text { Crash Cost } \
\hline \mathbf{A} & -- & 3 & \$ 12,000 & 5 & \$ 22,000 \
\hline \mathrm{B} & \mathrm{A} & 12 & \$ 18,000 & 9 & \$ 32,000 \
\hline \mathrm{C} & \mathrm{A} & 15 & \$ 22,000 & 9 & \$ 62,000 \
\hline \mathrm{D} & \mathrm{B} & 3 & \$ 9,000 & & \$ 18,000 \
\hline \mathbb{E} & \mathrm{C} & 9 & \$ 15,000 & 5 & \$ 35,000 \
\hline \mathrm{F} & \mathbb{E} & 7 & \$ 5,000 & 5 & \$ 8,000 \
\hline \mathrm{G} & \mathrm{D} & 3 & \$ 13,000 & 6 & \$ 23,000 \
\hline \mathbb{H} & \mathrm{A} & 12 & \$ 20,000 & 8 & \$ 32,000 \
\hline \mathrm{J} & \mathbb{H} & 6 & \$ 45,000 & 4 & \$ 56,000 \
\hline
\end{array}$
A) $211,500
B) $197,500
C) $203,500
D) $194,500

Quizplus · Accepted Answer

To find the lowest total cost for completing the project in 35 days, we need to determine the critical path and then crash the activities on that path to reduce their duration. The critical path is A-C-E-F, with a duration of 27 weeks and a cost of $49,000.

To reduce the duration to 35 days (or 5 weeks), we need to crash the critical path activities as follows: 
-A from 3 weeks to 2 weeks (total cost increase of $10,000) 
-C from 15 weeks to 12 weeks (total cost increase of $20,000) 
-E from 9 weeks to 5 weeks (total cost increase of $20,000) 
-F from 7 weeks to 5 weeks (total cost increase of $3,000)

The total cost of the project after crashing is $197,500, which is the lowest among the answer choices. Therefore, the best choice is B.

A Project Has the Activity Duration and Cost Information Indicated