A Partially Solved PERT Problem Is Detailed in the Table

question 10

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?

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Definitions:

Dissociation

A psychological condition where a person experiences a disconnection and lack of continuity between thoughts, memories, surroundings, actions, and identity.

Compensation

Remuneration and other benefits received in exchange for services rendered or as part of employment.

12-Hour Night Position

A work shift or scheduling system that entails personnel working through the night for a period of 12 hours.

Day/Evening Rotation

A work schedule that alternates between day and evening shifts, often seen in healthcare settings.