A project has the activity duration and cost information indicated in the table where all times are in weeks.There is a penalty of $250 per week for every week the project extends beyond 32 weeks.What is the cost of the least expensive project possible? $$\begin{array} { | l | l | l | l | l | l | }
\hline \text { Activity } & \begin{array} { l }
\text { Normal } \
\text { time }
\end{array} & \begin{array} { l }
\text { Crash } \
\text { time }
\end{array} & \begin{array} { l }
\text { Normal } \
\text { Cost }
\end{array} & \begin{array} { l }
\text { Crash } \
\text { Cost }
\end{array} & \text { Predecessor } \
\hline \mathrm { A } & 8 & 5 & \$ 1,000 & 2,000 & \
\hline \mathrm { B } & 6 & 4 & 1,500 & 2,000 & \text { A } \
\hline \mathrm { C } & 8 & 5 & 1,800 & 2,300 & \mathrm {~A} \
\hline \mathrm { D } & 12 & 9 & 1,000 & 1,800 & \mathrm {~B} \
\hline \mathrm { E } & 14 & 11 & 950 & 1,450 & \mathrm {~B} \
\hline \mathrm { F } & 9 & 7 & 1,500 & 1,900 & \text { C, D } \
\hline \mathrm { G } & 7 & 5 & 2,300 & 2,800 & \text { E, F } \
\hline
\end{array}$$
A) $11,450
B) $12,450
C) $13,450.
D) $14,450

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 $250 per week for every week the project extends beyond 32 weeks.What is the cost of the least expensive project possible? $$\begin{array} { | l | l | l | l | l | l | } 
\hline \text { Activity } & \begin{array} { l } 
\text { Normal } \
\text { time }
\end{array} & \begin{array} { l } 
\text { Crash } \
\text { time }
\end{array} & \begin{array} { l } 
\text { Normal } \
\text { Cost }
\end{array} & \begin{array} { l } 
\text { Crash } \
\text { Cost }
\end{array} & \text { Predecessor } \
\hline \mathrm { A } & 8 & 5 & \$ 1,000 & 2,000 & \
\hline \mathrm { B } & 6 & 4 & 1,500 & 2,000 & \text { A } \
\hline \mathrm { C } & 8 & 5 & 1,800 & 2,300 & \mathrm {~A} \
\hline \mathrm { D } & 12 & 9 & 1,000 & 1,800 & \mathrm {~B} \
\hline \mathrm { E } & 14 & 11 & 950 & 1,450 & \mathrm {~B} \
\hline \mathrm { F } & 9 & 7 & 1,500 & 1,900 & \text { C, D } \
\hline \mathrm { G } & 7 & 5 & 2,300 & 2,800 & \text { E, F } \
\hline
\end{array}$$
A) $11,450
B) $12,450
C) $13,450.
D) $14,450

Quizplus · Accepted Answer

To find the least expensive project possible, we need to use the crashing method.
We start by crashing the critical path (A-C-F-G) until we reach the minimum project duration of 32 weeks.
The critical path has a normal duration of 25 weeks and a normal cost of $5,300.
Crashing activity A has the lowest cost per week, so we crash it from 8 weeks to 5 weeks at a cost of $1,000 + ($2,000 - $1,000)/(8 - 5) x (5 - 8) = $2,500.
Now the critical path is (A-C-E-G) with a duration of 29 weeks and a cost of $11,450 =$5,300 + $2,500 + $1,450 + $2,200.
Since the project duration is still more than 32 weeks, we need to continue crashing.
The next activity to crash is C, which has a cost of $500/week (=$2,300 - $1,800) and can be crashed to 4 weeks, saving 1 week in the critical path.
The new critical path is (A-B-D-F-G) with a duration of 32 weeks and a cost of $12,450 =$11,450 + $800 + $200.
Therefore, the least expensive project possible is $12,450.

A Project Has the Activity Duration and Cost Information Indicated