1. The problem asks for the domain of the profit function $$P(x) = 349x - 39600$$ where $$x$$ is the number of passengers on a 1980-mile flight with a maximum seating capacity of 200. 2. The domain of a function is the set of all possible input values ($$x$$) for which the function is defined. 3. Since $$x$$ represents the number of passengers, it must be a non-negative integer (you cannot have negative passengers or fractional passengers). 4. Also, the maximum number of passengers is limited by the plane's seating capacity, which is 200. 5. Therefore, the domain is all integers $$x$$ such that $$0 \leq x \leq 200$$. 6. Among the given options, option B states "all non-negative integers less than or equal to 200," which matches our domain. Final answer: The domain of $$P(x)$$ is all non-negative integers less than or equal to 200.