Texts: The

At a time, a boat can stop for gas and servicing simultaneously. Assume that the

arrival rate of boats at the dock is $0\mathrm{.}8$ boats per hour. $($Round your answers to four decimal places.$)$

$($a$)$ What is the probability that the boat dock will be idle? $0\mathrm{.}2000$

$($b$)$ What is the average number of boats that will be waiting for service? $0\mathrm{.}6400$

$($c$)$ What is the average time $($in hours$)$ a boat will spend waiting for service? $0\mathrm{.}1600$ hours

$($d$)$ What is the average time $($in hours$)$ a boat will spend at the dock? $0\mathrm{.}2400$ hours

Yes, since the average time a boat will spend at the dock is less than $10$ minutes.

$($f$)$ The manager of Fore and Aft Marina is interested in balancing good customer service with the cost of providing this service. To achieve this, the manager would like the customer's average time in the system to be as close to $10$ minutes as possible, but not exceeding $10$ minutes. Is enlarging the capacity of the dock to handle two boats at a time a good way of achieving this? No$,$ enlarging the capacity of the dock may not be the best way of achieving their goal.