An Airport Is Located Next to a Housing Development

An airport is located next to a housing development. Where X is the number of planes that land per day and Y is the number of houses in the housing development, profits of the airport are 36X - X² and profits of the developer are 42Y - Y² - XY. Let H₁ be the number of houses built if a single profit-maximizing company owns the airport and the housing development. Let H₂ be the number of houses built if the airport and the housing development are operated independently and the airport has to pay the developer the total "damages" XY done by the planes to the profits of the developer.

A) H₁ = 18 and H₂ = 20.
B) H₁ = 21 and H₂ = 16.
C) H₁ = H₂ = 16.
D) H₁ = 16 and H₂ = 21.
E) H₁ = 20 and H₂ = 24.

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