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.

a$.$ 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.

housings per hour

b$.$ 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?