The production process shown below consists of five stages. The numbers in parentheses are the times in minutes to complete one unit before it moves on to the next stage. The demand rate is $42$ units per hour.

a$.$ How many workers are needed at each stage if management wants a utilization of at least $90$ percent? Round your answers down to the nearest whole number.

Stage A: workers

Stage B: workers

Stage C: workers

Stage D: workers

Stage E: workers

b$.$ Suppose that the number of workers at each stage are as follows:

$\backslash$table$[[$Stage$,$Number of Workers$],[$A$,5],[$B$,3],[$C$,3],[$D$,3],[$E$,3]]$

What is the output rate at each stage? Round your answers to the nearest whole number.

Stage A: units$/$hour

Stage B: units$/$hour

Stage $C$ : units$/$hour

Stage D: units$/$hour

Stage E: units$/$hour

c$.$ Where is the bottleneck in this process?

The bottleneck is