#$2.$ Software Development at Landon Corporation. 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 tumed to PERT$/$CPM as an aid to scheduling the activities remaining before the new product can be brought to the market. $($MLOs $71-7-4)$

The project network is depicted in the following diagram.

$7\mathrm{.}7\mathrm{.}1-$Bus $190-$ Chapter $9$ Homework Problems $($MLOs $7\mathrm{.}1-7\mathrm{.}4)$

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

$\backslash$table$[[$Activity$,$Optimistic,Most Probable,Pessimistic$],[$A$,3\mathrm{.}0,4\mathrm{.}0,5\mathrm{.}0],[$B$,3\mathrm{.}0,3\mathrm{.}5,7\mathrm{.}0],[$C$,4\mathrm{.}0,5\mathrm{.}0,6\mathrm{.}0],[$D$,2\mathrm{.}0,3\mathrm{.}0,4\mathrm{.}0],[$E$,6\mathrm{.}0,10\mathrm{.}0,14\mathrm{.}0],[$F$,7\mathrm{.}5,8\mathrm{.}5,12\mathrm{.}5],[$G$,4\mathrm{.}5,6\mathrm{.}0,7\mathrm{.}5],[$H$,5\mathrm{.}0,6\mathrm{.}0,13\mathrm{.}0],[$I$,2\mathrm{.}0,2\mathrm{.}5,6\mathrm{.}0],[$J$,4\mathrm{.}0,5\mathrm{.}0,6\mathrm{.}0]]$

a$.$ Develop an activity schedule for this project and identify the critical path activities.

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?

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?