Problem $3(20$ pts$).$ A manufacturer of engine belts uses multipurpose manufacturing equipment to produce a

variety of products. A technician is employed to perform the setup operations needed to change the machines over

from one product to the next. The amount of time required to set up the machines is a random variable that follows

an exponential distribution with a mean of $20$ minutes. The number of machines requiring a new setup is a Poisson

random variable with an average of $2$ machines per hour will require setup $($i$.$e$.$ arrival rate per hour per machine

$=\frac{2}{5}).$ The technician is responsible for setups on $5$ machines.

a$.$ Compute the service rate per hour.

b$.$ What percentage of time is the technician idle, or not involved in setting up a machine?

c$.$ On average, how long is a machine out of operation while waiting for the next setup to be completed?

d$.$ If the company hires another, equally capable technician to perform setups on these machines, how long

on average would a machine be out of operation while waiting for the next setup to be completed?