$2.$An automobile emissions testing center has six $(6)$ inspectors and tests $50$ autos per hour. Each inspector can inspect twelve $(12)$ autos per hour. What is the center's utilization?$3.$An automobile emissions testing center has six $(6)$ inspectors and tests $50$ autos per hour. Each inspector can inspect twelve $(12)$ autos per hour. If the center wants a utilization of $90\%,$ how many inspectors are required?$4.$An automobile emissions testing center has six $(6)$ inspectors and tests $50$ autos per hour. Each inspector can inspect twelve $(12)$ autos per hour. What would the service rate need to be in order to achieve $90\%$ utilization?$5.$A company is able to process $300$ customer statements $($bills$)$ per day. The average processing time is six $(6)$ days. What is the average number of statements $($bills$)$ the company has in process at any time?$6.$A manufacturer's average work$-$in$-$process inventory for Part $1234$ is $1,250$ parts. The workstation produces parts at the rate of $150$ parts per day. What is the average amount of time a part spends at this workstation?$7.$A car rental company at a major airport has $70\%$ of its fleet of $200$ cars rented each day on average. Cars are rented for an average of $4$ days. How many rentals are processed each day on average?