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, $230$ pieces per minute; and outer bending, $100$ pieces per minute. Determine the hourly capacity of each process stage and the number of machines needed to meet an output rate of $28,000$ units per hour. Round your answers for the hourly capacity of each process stage to the nearest whole mumber. Round your answers up for the number of machines needed to a whole number.

Cutting process:

Hourly capacity:

$12000$

pieces$/$hour

Number of machines needed:

$3$

machine$($s$)$

Inner bending:

Hourly capacity:

$13800$

pieces$/$hour

Number of machines needed:

$3$

machine$($s$)$

Outer bending:

Hourly capacity:

$6000$

pieces$/$hour

Number of machines needed:

$5$

machine$($s$)$