Problem $2$: $10$ points

The production process shown in the figure below consists of five stages. The numbers in parentheses are the times in minutes to complete one unit before it moves onto the next stage. The demand rate is $36$ units per hour.

a$)$ How many workers are needed at each stage if management wants a utilization of at least $90\%($Hint$,$ first convert the number in parentheses into units per hour then use the formula in slide $6)$

b$)$ Suppose the number of workers at each stage are as follows, what is the output rate at each stage in units per hour? $($Hint: use formular in slide $6)$

$\backslash$table$[[$Stage$,$Number of Workers$],[$A$,3],[$B$,3],[$C$,5],[$D$,2],[$E$,4]]$

c$)$ Which one is the bottleneck in this process?