Tim$$ Urban, owner$/$manager of$$ Urban's Motor Court in Key$$ West, is considering outsourcing the daily room cleanup for his motel to$$ Duffy's Maid Service. Tim rents an average of $50$ rooms for each of $365$ nights$(365\backslash$times $50$ equals the total rooms rented for the$$ year$).$ Tim's cost to clean a room is $$13\mathrm{.}00.$ The$$ Duffy's Maid Service quote is $$18\mathrm{.}00$ per room plus a fixed cost of $$24,000$ for sundry items such as uniforms with the$$ motel's name.$$ Tim's annual fixed cost for$$ space, equipment, and supplies is $$60,000.$

Part $2$

Based on the given information related to costs for each of the$$ options, the crossover point for Tim$=72007200$ room nights $($round your response to the nearest whole $$number$).$

Part $3$

If the number of room nights is less than the crossover$$ point, then

not outsourcing

is the best option available to Tim.

Part $4$

Based on the given room nights that Tim expects to rent $(18,250),$ the best option is

outsourcing

$.$