A company runs food service concessions for sporting events throughout the country. Their marketing research department chose a particular football stadium to test market a new jumbo hot dog. It was found that the demand for the new hot dog is given approximately by $$p = 5 - \ln(x), \quad 5 \leq x \leq 500,$$ where $x$ is the number of hot dogs (in thousands) that can be sold during one game at a price of $p$ dollars. If the company pays 1 dollar for each hot dog, how should the hot dogs be priced to maximize the profit per game?

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