C&A uses a two$-$step process to make a part. The first step involves cutting with a machine that requires a $40-$minute setup time before the production of each batch. The cutting takes $30$ minutes per part. The second step is polishing the parts from cutting. The polishing takes $240$ minutes per part. C&A has $5$ workers to do the task. The demand rate is $3$ parts per hour. What is the maximum inventory between cutting and polishing $($in number of parts$)$ if C&A operates with batches of $200$ parts?

Group of answer choices

$200$

$100$

$75$

$37\mathrm{.}5$