points$)$The table below lists the activities required to complete an equipment installation project. Also included are expected $($normal$)$ activity times and variances, precedence requirements, normal costs at expected times, and the cost to expedite by $1$ week. Any activity can only be expedited by $1$ week maximum. Activity times $($in weeks$)$ and variances are

computed using most likely, optimistic, and pessimistic times. Activity $"$s$"$ represents the start of the project, but it has no time or cost value. $($a$)$ Draw the network diagram, labeling all activities and times. What is the expected duration of the project? $($b$)$ What is the probability the project can be finished within $30$ weeks? How much would it cost and which activities would you expedite to reduce the expected duration of the project by $($c$)1$ week? $?$

$\backslash$table$[[$Activity$,\backslash$table$[[$Immediate$],[$predecessor$]],\backslash$table$[[$Normal$],[$time$]],\backslash$table$[[$Expedited$],[$time$]],\backslash$table$[[$Normal$],[$cost $($$$)$