A flexible manufacturing system is used to produce four parts. The FMS consists of one load/unload station and two automated processing stations (processes X and Y). The number of servers for each station type is to be determined. The FMS also includes an automated conveyor system with individual carts to transport parts between servers. The carts move the parts from one server to the next, drop them off, and proceed to the next delivery task. Average time required per transfer is 3.5 minutes. The following table summarizes the FMS:

All parts follow the same routing, which is 1 ( 2 ( 3 ( 1. The product mix and processing times at each station are presented in the table below:

Required production is 10 parts per hour, distributed according to the product mix indicated. Use the bottleneck model to determine
(a) The minimum number of servers at each station and the minimum number of carts in the transport system that are required to satisfy production demand and
(b) The utilization of each station for the answers above.

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Station 1 Load and unload Station 2 Ps X Station 3 Process Y Station 4 Transport system Number of human servers (workers) to be determined Number of automated servers to be determined Number of automated servers to be determined Number of carts to be determined Productj Product mix Sttion Station Station Station Pj 0.1 0.3 0.4 0.2 3 min 15 min 25 min 2 min 3 min 40 min 20 min 2 min 3 min 20 n 10 2 min 3 min 30 5 2 min