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 as follows.

A project network is given with the starting point on the left and the finish point on the right with activities A through J$.$ The arcs between the activities are listed as follows.

Start to A and to B$.$

A to D$.$

B to C$,$ to E$,$ and to F$.$

C to D$.$

D to I.

E to G and to H$.$

F to J$.$

G to I.

H to J$.$

I to Finish.

J to Finish.

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 $8\mathrm{.}59\mathrm{.}513\mathrm{.}5$

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

H $6714$

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 $25$ weeks? $($You may need to use the appropriate technology to answer this question. Round your answer to four decimal places.$)$

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 $32$ weeks? $($You may need to use the appropriate technology to answer this question. Round your answer to four decimal places.$)$