A Partially Solved PERT Problem Is Detailed in the Table

question 105

Essay

A partially solved PERT problem is detailed in the table below. Times are given in weeks.
$\begin{array}{|c|c|c|c|c|c|c|}\hline\text { Activity } & \text { Preceding } & \begin{array}{c}\text { Optimistic } \\\text { Time }\end{array} & \begin{array}{c}\text { Probable } \\\text { Time }\end{array} & \begin{array}{c}\text { Pessimistic } \\\text { Time }\end{array} & \begin{array}{c}\text { Expected } \\\text { Time }\end{array} & \text { Variance } \\\hline \mathrm{A} & -- & 7 & 9 & 14 & & 1.361 \\\hline \mathrm{B} & \mathrm{A} & 2 & 2 & 8 & & 0 \\\hline \mathrm{C} & \mathrm{A} & 8 & 12 & 16 & & 0 \\\hline \mathrm{D} & \mathrm{A} & 3 & 5 & 10 & & 1.361 \\\hline \mathrm{E} & \mathrm{B} & 4 & 6 & 8 & & 0 \\\hline \mathrm{F} & \mathrm{B} & 6 & 8 & 10 & & 0 \\\hline \mathrm{G} & \mathrm{C}, \mathrm{F} & 2 & 3 & 4 && 0 \\\hline \mathrm{H} & \mathrm{D} & 2 & 2 & 8 & & 1.000 \\\hline \mathrm{I} & \mathrm{H} & 6 & 8 & 16 & & 2.778 \\\hline \mathrm{J} & \mathrm{G}, \mathrm{I} & 4 & 6 & 14 & & 2.778 \\\hline \mathrm{K} & \mathrm{E}, \mathrm{J} & 2 & 2 & 5 & & 0.250 \\\hline\end{array}$ 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?

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Definitions:

Optically Active

Refers to a substance that is capable of rotating the plane of polarized light, indicating the presence of chiral molecules.

Bicyclic Compounds

Organic compounds that contain two fused or connected rings in their molecular structure.

Diene

Organic compounds containing two double bonds, which may participate in a variety of chemical reactions, especially polymerization.

Dienophile

A chemical compound that acts as an electron-deficient partner in Diels-Alder reactions, typically containing double or triple bonds.