Mary Yetter,a Staff Analyst at the Los Angeles Plant of Computer

Mary Yetter,a staff analyst at the Los Angeles plant of Computer Products Corporation,is assigned to the team that is developing the process design for producing the bar code scanner of Example 1.The corporate planning group in San Jose,California has contacted her and has asked how confident the design group is about completing the project in 60 days.She has developed these estimated time durations in days for the project: $$\begin{array} { c c c c c } \hline \hline \text { Activity } & \begin{array} { c } \text { Immediate } \\\text { Predecessor } \\\text { Activities }\end{array} & \begin{array} { c } \text { Optimistic } \\\text { Time } \left( t _ { 0 } \right)\end{array} & \begin{array} { c } \text { Most Likely } \\\text { Time } \left( t _ { \mathrm { m } } \right)\end{array} & \begin{array} { c } \text { Pessimistic } \\\text { Time } \left( t _ { \mathrm { p } } \right)\end{array} \\\hline \text { A } & - & 10 & 12 & 15 \\\text { B } & \text { A } & 6 & 10 & 14 \\\text { C } & \text { A } & 10 & 15 & 20 \\\text { D } & \text { A } & 9 & 9 & 18 \\\text { E } & \text { B } & 5 & 6 & 8 \\\text { F } & \text { C,E } & 10 & 12 & 13 \\\text { G } & \text { B } & 12 & 14 & 16 \\\text { H } & \text { B,D } & 18 & 21 & 24 \\\text { I } & \text { B,D } & 10 & 15 & 20 \\\text { J } & \text { F.G.H } & 8 & 10 & 14 \\\hline \hline\end{array}$$
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 58 days to complete?
d. Which path in the project network offers the greatest risk of overrunning a new deadline of 56 days?