SOLUTION: A company runs food device concessions for sporting events throughout the country their marketing research department chose a particular football stadium to test market a nwe jumbo
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Question 1180888: A company runs food device concessions for sporting events throughout the country their marketing research department chose a particular football stadium to test market a nwe jumbo hot dog. It was found that the demand for the new hot dog is given approximately by : p=4-ln(x),5 is less than equal to x and x is less than equal to 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 hot dogs be priced to maximize the profit per game?
Answer by Solver92311(821) (Show Source): You can put this solution on YOUR website!
Price as a function of demand: \ =\ 4\ -\ \ln(x))
Revenue: \ =\ xp(x))
Cost: \ =\ x)
Profit: \ =\ R(x)\ -\ C(x)\ =\ x\(4\ -\ \ln(x)\)\ -\ x)
\ =\ x\(3\ -\ \ln(x)\))
)
\ =\ 0\ \Right\ x\ =\ e^2)
Hence 
is maximum demand, so the price at maximum demand is
\ =\ 4\ -\ \ln\(e^2\)\ =\ 2\ \ )
dollars.
John
My calculator said it, I believe it, that settles it
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