A company runs food service concessions for sporting events throughout the count

Question

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=4-ln(x), 5< are also equal to but i cant show it with typing) 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?

Explanation / Answer

So the funcion you want to optimize is profit. Lets call P(x) the profit when selling x-thousand hot dogs. P(x)=x(4-ln(x))-1x because x(4-ln(x)) is the number sold times the price, or income, and 1x is the cost of each hot dog. Income-cost=profit, so you are looking to maximize P(x) P(x)=x(4-ln(x))l1x=x(4-ln(x)-1)=x(3-ln

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