Aquatica makes underwater camera housings for divers. The process begins with a solid rectangular block of aluminum that is used to make a single housing. A computer numerically controlled (CNC) machine drills into the block to make the metal “frame” of the housing. Each block requires 15 minutes of drilling. The frame is then chemically treated in a series of baths. There is ample capacity in the treating stage. Finally, a worker must manually attach the various buttons and components to the metal housing. This assembly takes 120 minutes per housing per worker and Aquatica has 6 workers trained to do this task. The CNC machine requires a 30-minute setup time before the production of a batch can begin. 

a. If the CNC machine produces 14 housings between setups, what would be its capacity (in housings per hour)? 

b. Assuming the process is supply-constrained, what is the utilization (as a number between 0 and 1) of the CNC machine if it operates in batches of 14 housings? 

c. Assuming the process is supply-constrained and operates with batches of 14 housings, what is the average inventory of housings? 

d. Aquatica actually makes five different housings. As already mentioned, the CNC machine must be set up whenever production switches from one housing to the other. In each case, the setup time is 30 minutes and it takes 15 minutes to drill the block for each type of housing. Demands for the housings are given in Table 7.7. 

If it wishes to minimize inventory while satisfying its demand, how many D7000 housings should it produce in each batch?

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TABLE 7.7 Demand Rate (housings per hour) Housing Type D7000 0.4 5DS Mark III 0.5 AN-5n 0.6 D300 0.7 T2i 0.8