The Stone River Textile Mill was inspected by OSHA and found to be in violation of a number of safety regulations. The OSHA inspectors ordered the mill to alter some existing machinery to make it safer (e.g., add safety guards); purchase some new machinery to replace older, dangerous machinery; and relocate some machinery to make safer passages and unobstructed entrances and exits. OSHA gave the mill only 35 weeks to make the changes; if the changes were not made by then, the mill would be fined \( \$ 300,000 \). The mill determined the activities in a PERT network that would have to be completed and then estimated the indicated activity times, as shown in the table below. Construct the PERT network for this project using the following table:
\begin{tabular}{|c|c|c|c|c|c|}
\hline \multirow[b]{2}{*}{Activity} & \multirow[b]{2}{*}{Description} & \multirow[t]{2}{*}{\begin{tabular}{l}
Activity \\
Predecessor
\end{tabular}} & \multicolumn{3}{|r|}{\begin{tabular}{l}
Time \\
Estimates \\
(Weeks)
\end{tabular}} \\
\hline & & & a & m & b \\
\hline a & Order new machinery & - & 1 & 2 & 3 \\
\hline b & Plan new physical layout & - & 2 & 5 & 8 \\
\hline c & Determine safety changes in existing machinery & - & 1 & 3 & 5 \\
\hline d & Receive equipment & a & 4 & 10 & 25 \\
\hline e & Hire new employees & a & 3 & 7 & 12 \\
\hline f & Make plant alterations & b & 10 & 15 & 25 \\
\hline \( g \) & Make Changes in existing machinery & c & 5 & , & 14 \\
\hline h & Irain new employees & d,e & 2 & 3 & 7 \\
\hline i & Install new machinery & d, e, 1 & 1 & 4 & 6 \\
\hline I & Relocate old machinery & d, e, f,g & 2 & 5 & 10 \\
\hline k & Conduct employee satety orientation & h, i,j & 2 & 2 & 2 \\
\hline
\end{tabular}
a. Compute the expected activity time, ES, EF, LF, LS, S and the variance of each activity. Summarize your results in a table. The details of the calculations must not be included in the table.
b. Determine the project critical path and its expected duration.
c. What is the probability that the mill will be fined \( \$ 300,000 \) ?
