A Project Has the Following Activities,precedence Relationships,and Time Estimates in Weeks

Essay

A project has the following activities,precedence relationships,and time estimates in weeks: $$\begin{array} { c c c c c } \text { Activity } & \begin{array} { c } \text { Immediate } \\\text { Predecessor } \\\text { Activities }\end{array} & \begin{array} { c } \text { Optimistic } \\\text { Time } \left( t _ { 0 } \right)\end{array} & \begin{array} { c } \text { Most Likely } \\\text { Time } \left( t _ { \mathrm { m } } \right)\end{array} & \begin{array} { c } \text { Pessimistic } \\\text { Time } \left( t _ { \mathrm { p } } \right)\end{array} \\\hline \text { A } & - \cdot & 15 & 20 & 25 \\\text { B } & - & 8 & 10 & 12 \\\text { C } & \text { A } & 25 & 30 & 40 \\\text { D } & \text { B } & 15 & 15 & 15 \\\text { E } & \text { B } & 22 & 25 & 27 \\\text { F } & \text { E } & 15 & 20 & 22 \\\text { G } & \text { D } & 20 & 20 & 22 \\\hline \hline\end{array}$$
a. Compute the expected time and variance for each activity.
b. Determine the critical path and the expected duration of the project.
c. What is the probability that the project will take longer than 56 weeks to complete?