Q$5\mathrm{.}7($PTests$)$ Precision Testing $($PTests$)$ does fluid testing for several local hospitals. Consider their urine testing process. Each sample

requires $12$ seconds to test, but after $300$ samples, the equipment must be recalibrated. No samples can be tested during the

recalibration process and that process takes $30$ minutes.

a$.$ What is PTests's maximum capacity to test urine samples $($in samples per hour$)?[5\mathrm{.}1]$

b$.$ Suppose $2\mathrm{.}5$ urine samples need to be tested per minute. What is the smallest batch size $($in samples$)$ that ensures that the process is

not supply constrained? $($Note; A batch is the number of tests between calibrations.$)[5\mathrm{.}6]$