$33$ Software Development Specialists $($SDS$)$ is in$-$ volved with developing software for customers in the banking industry. SDS breaks a large program$-$ ming project into teams that perform the necessary steps. Team A is responsible for going from general systems design all the way through to actual systems testing. This involves $18$ separate activities. Team B is then responsible for the final installation.

To determine cost and time factors, optimistic, most likely, and pessimistic time estimates have been made for all of the $18$ activities involved for team A$.$

The first step that this team performs is general sys$-$ tems design. The optimistic, most likely, and pessi$-$ mistic times are $3,4,$ and $5$ weeks. Following this, a number of activities can begin. Activity $2$ is involved with procedures design. Optimistic, most likely, and pessimistic times for completing this activity are $4,5,$ and $12$ weeks. Activity $3$ is developing detailed report designs. Optimistic, most likely, and pessimis$-$ tic time estimates are $6,8,$ and $10$ weeks. Activity $4,$ detailed forms design, has optimistic, most likely, and pessimistic time estimates of $2,5,$ and $5$ weeks.

Activities $5$ and $6$ involve writing detailed pro$-$ gram specifications and developing file specifications. The three time estimates for activity $5$ are $6,7,$ and $8$ weeks, and the three time estimates for activity $6$ are $3,4,$ and $5$ weeks. Activity $7$ involves specifying system test data. Before this is done, activity $6,$ involv$-$ ing file specifications, must be completed. The time estimates for activity $7$ are $2,3,$ and $7$ weeks. Activity $8$ involves reviewing forms. Before activity $8$ can be conducted, detailed forms design must be completed. The time estimates for activity $8$ are $3,3,$ and $9$ weeks. The next activity, activity $9,$ is reviewing the detailed report design. This requires that the detailed report design, activity $3,$ be completed first. The time esti$-$ mates for activity $9$ are $1,3,$ and $5$ weeks, respectively.

Activity $10$ involves reviewing procedures de$-$ sign. Time estimates are $1,2,$ and $9$ weeks. Of course, procedures design must be done before activity $10$ can be started. Activity $11$ involves the system de$-$ sign checkpoint review. A number of activities must be completed before this is done. These activities include reviewing the forms, reviewing the detailed report design, reviewing the procedures design, writ$-$ ing detailed program specs, and specifying system test data. The optimistic, most likely, and pessimistic time estimates for activity $11$ are $3,4,$ and $5$ weeks. Performing program logic design is activity $12.$ This can be started only after the system design checkpoint review is completed. The time estimates for activity $12$ are $4,5,$ and $6$ weeks.

Activity $13,$ coding the programs, is done only after the program logic design is completed. The time estimates for this activity are $6,10,$ and $14$ weeks. Ac$-$ tivity $14$ is involved in developing test programs. Activ$-$ ity $13$ is the immediate predecessor. Time estimates for activity $14$ are $3,4,$ and $11$ weeks. Developing a system test plan is activity $15.$ A number of activities must be completed before activity $15$ can be started. These ac$-$ tivities include specifying system test data, writing de$-$ tailed program specifications, and reviewing procedure designs, the detailed report design, and forms. The time estimates for activity $15$ are $3,4,$ and $5$ weeks.

Activity $16,$ creating system test data, has time estimates of $2,4,$ and $6$ weeks. Activity $15$ must be done before activity $16$ can be started. Activity $17$ is reviewing program test results. The immedi$-$ ate predecessor to activity $17$ is to test the programs $($activity $14).$ The three time estimates for activity $17$ are $2,3,$ and $4$ weeks. The final activity is conducting system tests. This is activity $18.$ Before activity $18$ can be started, activities $16$ and $17$ must be complete. The three time estimates for conducting these system tests are $2,6,$ and $7$ weeks.

How long will it take for team A to complete its programming assignment?