Consider the barber shop problem defined in problem $(2)$ of section

$7\mathrm{.}2.$ Determine the following:

$($a$)$ the long$-$run average number of customers being serviced

$($b$)$ the long$-$run average number of customers in the shop

$($c$)$ the long$-$run proportion of time both barbers are busy

$($d$)$ the long$-$run number of lost customers per hour