Acompany 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 = 4 - \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?