$8\mathrm{.}1$ Peter's Paper Clips uses a three$-$stage production process: cutting wire to prescribed lengths, inner bending, and outer bending. The cutting prucess can produce at a rate of $200$ pieces per minute; inner bending, $160$ pieces per minule; and auter bending, $150$ pieces per minute. Determine the hourly capacity of each process stage and the number of machines needed to meet an output rate of $20,0100$ uniss per hour. How does facility layout impact your mumencal analyses and proeess effictency? Explain.