Late each summer, migrating rufous hummingbirds stop in Arizona, where they establish and defend territories. Larger territories contain more flowers, provide more energy in the form of nectar, and are harder to defend. Researchers Astrid Kodric$-$Brown and James Brown developed a cost$-$benefit model to help explain observed variation in territory size $($S$).$ A modified version of their model is shown to the right.

Based on this model$$and assuming optimal behavior$$how large an area should a hummingbird defend $($referring to labels on the x$-$axis$)?$