$10-27.$ ESTIMATING A COST FUNCTION, HIGH$-$LOW

METHOD. Roy Travel offers helicopter service from suburban towns to John F$.$ Kennedy International Airport in New York City. Each of its nine helicopters makes between $1,350$ and $2,100$ round$-$trips per year. The records indicate that a helicopter that has made $1,350$ round$-$trips in the year incurs an average operating cost of $\backslash (\backslash$$ $450\backslash )$ per round$-$trip, and one that has made $2,100$ round$-$trips in the year incurs an average operating cost of $\backslash (\backslash$$ $350\backslash )$ per round$-$trip.

Required

$1.$ Using the high$-$low method, estimate the linear relationship $\backslash ($ y$=$a$+$b X $\backslash ),$ where $\backslash ($ y $\backslash )$ is the total annual operating cost of a helicopter and $\backslash ($ X $\backslash )$ is the number of round$-$trips it makes to JFK airport during the year.

$2.$ Give examples of costs that would be included in $\backslash ($ a $\backslash )$ and in $\backslash ($ b $\backslash ).$

$3.$ If Roy Travel expects each helicopter to make, on average, $1,700$ round$-$trips in the coming year, what should be its estimated operating budget for the helicopter fleet?