As the Director of Concessions at the local ballpark, Mike is responsible for ordering items for the concession stands to ensure there is sufficient supply for game day. Past experience suggests he can assume game day demand for hot dogs follows a normal distribution with an average of 18,000 and a standard deviation of 400.

The concession stands sell hot dogs to fans for $5.50. The price of the hot dog is $0.50 each and the cost of buns cost $0.18 each. There is associated miscellaneous cost of $0.32 for each hot dog that's sold (condiments, napkins, etc.). Hot dog buns that aren't sold can be returned to the supplier for a credit of $0.04 each. There is no opportunity to return the unsold hot dogs.

Based on the information above, what is the optimal number of hot dogs (and buns) Mike should purchase for each home game?