Air Canuck$’$s operations at Diefenbaker Airport are supported by four de$-$icing bays dedicated to Air Canuck. Other airlines are not permitted to use Air Canuck$’$s de$-$icing bays. At peak travel times during the day, Air Canuck schedules aircraft departures such that they arrive at the de$-$icing station exactly four minutes apart. On inclement weather days, all of those aircraft must be de$-$iced prior to departure. On average, $15$ minutes are required to de$-$ice an aircraft. The coefficient of variation of aircraft de$-$icing times is $1.$

a$)$ During this peak departure period, what is the expected time an aircraft will spend waiting for de$-$icing?

b$)$ In total, how many aircraft are at the de$-$icing station?

A de$-$icing bay is staffed by a team of three employees $–$ each paid $$20/$hr$.$ The cost of renting the tarmac space big enough for a de$-$icing bay is $$1000/$hr$.$ Air Canuck operates primarily the Airbus A$320,$ having two engines. Each engine burns approximately $320$ kg$/$hr of jet fuel while idling or taxiing. A single kg of jet fuel costs $$1\mathrm{.}35.$

c$)$ How much money would Air Canuck save$/$lose by adding another de$-$icing bay? $($Note: Aircraft$’$s engines continue to operate during de$-$icing.$)$