A single machine is used to make two components, let's call them A and B. It takes 249 seconds to switch over from A to B or from B to A. During that time, no production occurs. When in production, each unit of A takes 0.4 seconds to be completed, while each unit of B takes 0.7 seconds.
The machine switches back and forth between producing a batch of A and a batch of B. For now, assume that the batch sizes for both products are set to 600 units, and that kits are made as fast as the machine allows. (A kit consists of one part A and one part B, see part d below).
a) What is the capacity of the machine expressed in kits per minute with the given batch sizes?
b) What is the utilization of the machine?
c) What is the average inventory of B?
d) A kit of one component A and one component B can be assembled into a single part C in an assembly process with a capacity of 29.4 parts C per minute. What batch size should be used for A and B to produce kits at exactly this rate while minimizing inventories?