The builder of a new movie theater complex is trying to decide how many screens she wants. Below are her estimates of the number of patrons the complex will attract each year, depending on the number of screens available.

Number of screens Total number of patrons

$140,000$

$270,000$

$395,000$

$4115,000$

$5130,000$

After paying the movie distributors and meeting all other noninterest expenses, the owner expects to net $$3$ per ticket sold. Construction costs are $$1,000,000$ per screen.