You may need to use the appropriate technology to answer this question.

The product development group at Landon Corporation has been working on a new computer software product that has the potential to capture a large market share. Through outside sources, Landon's management learned that a competitor is working to introduce a similar product. As a result, Landon's top management increased its pressure on the product development group. The group's leader turned to PERT$/$CPM as an aid to scheduling the activities remaining before the new product can be brought to the market.

The project network is depicted in the following diagram.

A project network with $12$ activities and $15$ directed arcs is shown.

Activity Start is connected to activity A and to activity B$.$

Activity A is connected to activity D$.$

Activity B is connected to activity C$,$ to activity E$,$ and to activity F$.$

Activity C is connected to activity D$.$

Activity D is connected to activity I.

Activity E is connected to activity G and to activity H$.$

Activity F is connected to activity J$.$

Activity G is connected to activity I.

Activity H is connected to activity J$.$

Activity I is connected to activity Finish.

Activity J is connected to activity Finish.

Activity Finish has no arcs directed to other activities.

The activity time estimates $($in weeks$)$ are listed in the following table.

Activity Optimistic Most Probable Pessimistic

A $345$

B $33\mathrm{.}57$

C $456$

D $234$

E $71013$

F $6\mathrm{.}57\mathrm{.}511\mathrm{.}5$

G $4\mathrm{.}567\mathrm{.}5$

H $4512$

I $22\mathrm{.}56$

J $456$

$($a$)$

Develop an activity schedule for this project and identify the critical path activities. $($Enter your answers as a comma$-$separated list.$)$

$($b$)$

Based solely on the critical path, what is the probability that the project will be completed so that Landon Corporation may introduce the new product within $24$ weeks? $($Round your answer to four decimal places.$)$

$($c$)$

Based solely on the critical path, what is the probability that the project will be completed so that Landon Corporation may introduce the new product within $30$ weeks? $($Round your answer to four decimal places.$)$