PA $7-10($Static$)$ Aquatica makes underwater camera housings...

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.

Housing Type Demand Rate $($housings per hour$)$

D$70000\mathrm{.}4$

$5$DS Mark III $0\mathrm{.}5$

AN$-5$n $0\mathrm{.}6$

D$3000\mathrm{.}7$

T$2$i $0\mathrm{.}8$

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

Note: Round your answer to $1$ decimal place.

Assuming the process is supply constrained, what is the utilization $($as a percentage$)$ of the CNC machine if it operates in batches of $14$ housings?

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

Note: Round your answer to $2$ decimal places.

Aquatica actually makes $5$ 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 the table above. If it wish to minimize inventory while satisfying its demand, how many D$7000$ housings should it produce in each batch?