In A Machine Cluster The Appropriate Number Of Production Machines

In a machine cluster, the appropriate number of production machines to assign to the worker is to be determined. Let n = the number of machines. Each production machine is identical and has an automatic processing time Tm = 4.0 min. The servicing time Ts = 12 sec for each machine. The full cycle time for each machine in the cell is Tc = Ts + Tm. The repositioning time for the worker is given by Tr = 5 + 3n, where Tr is in sec. Tr increases with n because the distance between machines increases with more machines.
(a) Determine the maximum number of machines in the cell if no machine idle time is allowed. For your answer, compute
(b) The cycle time and
(c) The worker idle time expressed as a percent of the cycle time?

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