answer question and provide assumptions Problem $3(35$ points$)$

The Dynaco Manufacturing Company produces a particular product in an assembly line operation. One of the machines on the line is a drill press that has a single assembly line feeding into it$.$ A partially completed unit arrives at the press to be worked on every $7\mathrm{.}5$ minutes, on average. The machine operator can process an average of $10$ parts per hour.

a$)$ Calculate the average number of units in the system $($waiting and being serviced$).$

b$)$ Calculate the average time a component spends in the system

c$)$ If management wants to have its operators working $95\%$ of the time. What must the assembly arrival rate be for the operators to be as busy as management would like.