A gentleman farmer maniacally works on academic projects to raise funds for his true passion,farming.He has identified seven tasks and developed three time estimates (all in days)of the next big project on the farm,replacing the fence at the comedy pasture.Tasks,precedence requirements,and time estimates are shown in the table.What is the probability that the project is completed in 31 days? $\begin{array}{|l|l|l|l|l|}
\hline \text { Activity } & \begin{array}{l}
\text { Optimistic } \
\text { time }
\end{array} & \begin{array}{l}
\text { Most Likely } \
\text { time }
\end{array} & \begin{array}{l}
\text { Pessimistic } \
\text { time }
\end{array} & \text { Predecessor } \
\hline \text { Corner Posts } & 4 & 5 & 6 & \text { - } \
\hline \text { String Line } & 7 & 8 & 9 & - \
\hline \text { Dig Holes } & 10 & 12 & 14 & \text { Corner Posts } \
\hline \text { Plant Posts } & 11 & 14 & 17 & \text { String Line } \
\hline \text { Weld Top Bar } & 8 & 11 & 14 & \text { String Line } \
\hline & & & & \text { Dig Holes, Plant } \
\text { Paint } & 9 & 11 & 13 & \text { Posts } \
\hline \text { Tack Wire } & 9 & 12 &16& \text { Weld Top Bar } \
\hline
\end{array}$

A)0.055
B)0.092
C)0.125
D)0.187

Question

A gentleman farmer maniacally works on academic projects to raise funds for his true passion,farming.He has identified seven tasks and developed three time estimates (all in days)of the next big project on the farm,replacing the fence at the comedy pasture.Tasks,precedence requirements,and time estimates are shown in the table.What is the probability that the project is completed in 31 days? $\begin{array}{|l|l|l|l|l|}
\hline \text { Activity } & \begin{array}{l}
\text { Optimistic } \
\text { time }
\end{array} & \begin{array}{l}
\text { Most Likely } \
\text { time }
\end{array} & \begin{array}{l}
\text { Pessimistic } \
\text { time }
\end{array} & \text { Predecessor } \
\hline \text { Corner Posts } & 4 & 5 & 6 & \text { - } \
\hline \text { String Line } & 7 & 8 & 9 & - \
\hline \text { Dig Holes } & 10 & 12 & 14 & \text { Corner Posts } \
\hline \text { Plant Posts } & 11 & 14 & 17 & \text { String Line } \
\hline \text { Weld Top Bar } & 8 & 11 & 14 & \text { String Line } \
\hline & &  &  & \text { Dig Holes, Plant } \
 \text { Paint } & 9 & 11 & 13 & \text { Posts } \
\hline \text { Tack Wire } & 9 & 12 &16& \text { Weld Top Bar } \
\hline
\end{array}$

A)0.055
B)0.092
C)0.125
D)0.187

Quizplus · Accepted Answer

The critical path is Corner Posts-Dig Holes-Plant Posts-Weld Top Bar-Tack Wire, with a duration of 31 days. The probability of completing the project in 31 days is the probability that all activities on the critical path are completed in their most likely times. This probability is calculated as follows:P(completion in 31 days) = P(Corner Posts in 5 days) * P(Dig Holes in 12 days) * P(Plant Posts in 14 days) * P(Weld Top Bar in 11 days) * P(Tack Wire in 12 days)= 0.6 * 0.5 * 0.4 * 0.7 * 0.5= 0.055

A Gentleman Farmer Maniacally Works on Academic Projects to Raise