$11\mathrm{.}1$ The production process shown in Exhibit $11\mathrm{.}27$ 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 $36$ units per hour.

Exhibit $11\mathrm{.}27$ Process Flow for Problem $35$

Details

a$.$ How many workers are needed at each stage if management wants a utilization of at least $90$ percent?

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

Stage

Number of Workers

A

$3$

B

$3$

C

$5$

D

$2$

E

$4$

What is the output rate at each stage?