$1$Peter's Paper Clips uses a three$-$stage production process: cutting wire to prescribed lengths, inner bending, and outer bending. The cutting process can produce at a rate of $200$ pieces per minute; inner bending, $160$ pieces per minute; and outer 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 $20,000$ units per hour. How does facility layout impact your numerical analysis and process efficiency? Explain.

$2.$ Calculate the minimum number of workstations required.

$3.$ What happens to the assembly line efficiency and idle time when you add an additional work station $(5$ work stations$).$ How many workstations would you recommend.