A group technology cell is organized to produce a particular family of products. The cell consists of three processing stations, each with one server; an assembly station with 3 servers; and a load/unload station with 2 servers. A mechanized transfer system moves the products between stations. The transfer system has a total of 6 transfer carts. Each cart includes a work holder that holds the products during their processing and assembly, and therefore, each cart must remain with the product throughout processing and assembly. The cell resources can be summarized as follows:

The GT cell is currently used to produce four products. All products follow the same routing, which is 1 ( 2 ( 3 ( 4 ( 5 ( 1. The product mix and station times for the parts are presented in the table below:

The average transfer between stations takes 2 minutes in addition to the time spent at the workstation.
(a) Determine the bottleneck station in the GT cell and the critical value of N. Compute the overall production rate and manufacturing lead time of the cell, given that the number of parts in the system = N*. If N* is not an integer, use the integer that is closest to N*.
(b) Compute the overall production rate and manufacturing lead time of the cell, given that the number of parts in the system = N* + 10. If N* is not an integer, use the integer that is closest to N* + 10.
(c) Compute the utilizations of the six stations.

Station Description Number of servers 1Load and unload 2 workers 2 Process 3 Process Y 4 Process 5 Assembly l server l server 1 server 3 workers 6 cariers Transport system Productj Product mix Station Station Station Station Station Station 3 5 2 4 Pj 0.35 0.25 0.10 0.30 4 min 8 min 5 min 7 min 18 min 2.5 min 4 min 4 min 8 min 6 min 14 min 2.5 min 4 min 2 in 6 5n 1 2.5 min 4 min 6 7 min 10 min 12 in 2.5 min