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 33 weeks? $$\begin{array} { | l | l | l | l | l | l | }
\hline \text { Activity } & \begin{array} { l }
\text { Normal } \
\text { time }
\end{array} & \begin{array} { l }
\text { Crash } \
\text { time }
\end{array} & \begin{array} { l }
\text { Normal } \
\text { Cost }
\end{array} & \begin{array} { l }
\text { Crash } \
\text { Cost }
\end{array} & \text { Predecessor } \
\hline \mathrm { A } & 8 & 5 & \$ 1,000 & 2,000 & \
\hline \mathrm { B } & 6 & 4 & 1,500 & 2,000 & \text { A } \
\hline \mathrm { C } & 8 & 5 & 1,800 & 2,300 & \mathrm {~A} \
\hline \mathrm { D } & 12 & 9 & 1,000 & 1,800 & \mathrm {~B} \
\hline \mathrm { E } & 14 & 11 & 950 & 1,450 & \mathrm {~B} \
\hline \mathrm { F } & 9 & 7 & 1,500 & 1,900 & \text { C, D } \
\hline \mathrm { G } & 7 & 5 & 2,300 & 2,800 & \text { E, F } \
\hline
\end{array}$$
A) $11,250
B) $11,500
C) $12,250
D) $12,500

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 33 weeks? $$\begin{array} { | l | l | l | l | l | l | } 
\hline \text { Activity } & \begin{array} { l } 
\text { Normal } \
\text { time }
\end{array} & \begin{array} { l } 
\text { Crash } \
\text { time }
\end{array} & \begin{array} { l } 
\text { Normal } \
\text { Cost }
\end{array} & \begin{array} { l } 
\text { Crash } \
\text { Cost }
\end{array} & \text { Predecessor } \
\hline \mathrm { A } & 8 & 5 & \$ 1,000 & 2,000 & \
\hline \mathrm { B } & 6 & 4 & 1,500 & 2,000 & \text { A } \
\hline \mathrm { C } & 8 & 5 & 1,800 & 2,300 & \mathrm {~A} \
\hline \mathrm { D } & 12 & 9 & 1,000 & 1,800 & \mathrm {~B} \
\hline \mathrm { E } & 14 & 11 & 950 & 1,450 & \mathrm {~B} \
\hline \mathrm { F } & 9 & 7 & 1,500 & 1,900 & \text { C, D } \
\hline \mathrm { G } & 7 & 5 & 2,300 & 2,800 & \text { E, F } \
\hline
\end{array}$$
A) $11,250
B) $11,500
C) $12,250
D) $12,500

Quizplus · Accepted Answer

The critical path is A-B-D-F-G with a normal duration of 42 weeks. To reduce the project duration to 33 weeks, we need to crash 9 weeks. The least expensive way to crash is to reduce activities with the lowest crash cost per week. By crashing A (3 weeks), B (2 weeks), D (3 weeks), and F (1 week), the total cost is $12,250.

A Project Has the Activity Duration and Cost Information Indicated