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 = 7 - ln(x) when 5 ≤ x ≤ 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?