A Partially Solved PERT Problem Is Detailed in the Table

Essay

A partially solved PERT problem is detailed in the table below. Times are given in weeks.
$\begin{array}{|c|c|c|c|c|c|l|}\hline\text { Activity } & \text { Preceding } & \begin{array}{c}\text { Optimistic } \\\text { Time }\end{array} & \begin{array}{c}\text { Probable } \\\text { Time }\end{array} & \begin{array}{c}\text { Pessimistic }\\\text { Time }\end{array} & \begin{array}{c}\text { Expected } \\\text { Time }\end{array} & \text { Variance } \\\hline \mathrm{A} & -- & 7 & 9 & 14 & & 1.361 \\\hline \mathrm{B} & \mathrm{A} & 2 & 2 & 8 & & 0 \\\hline \mathrm{C} & \mathrm{A} & 8 & 12 & 16 & & 0 \\\hline \mathrm{D} & \mathrm{A} & 3 & 5 & 10 & & 1.361 \\\hline \mathrm{E} & \mathrm{B} & 4 & 6 & 8 & & 0 \\\hline \mathrm{F} & \mathrm{B} & 6 & 8 & 10 & & 0 \\\hline \mathrm{G} & \mathrm{C}, \mathrm{F} & 2 & 3 & 4 & & 0 \\\hline \mathrm{H} & \mathrm{D} & 2 & 2 & 8 & & 1.000 \\\hline \mathrm{I} & \mathrm{H} & 6 & 8 & 16 & & 2.778 \\\hline \mathrm{J} & \mathrm{G}, \mathrm{I} & 4 & 6 & 14 & & 2.778 \\\hline \mathrm{K} & \mathrm{E}, \mathrm{J} & 2 & 2 & 5 & & 0.250 \\\hline\end{array}$
a. Calculate the expected time for each activity. Enter these values in the appropriate column in the table above.
b. Which activities form the critical path?
c. What is the estimated time of the critical path?
d. What are the project variance and the project standard deviation?
e. What is the probability of completion of the project after week 40?