A company runs food service concessions for sporting events throughout the country. Their marketing research department chose a particular football stadiumt to test market a new jumbo hot dog. It was found that the demand for the new hot dog is given approximately by p=6-ln(x), 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? Price = __________

Question
Asked Nov 13, 2019
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A company runs food service concessions for sporting events throughout the country. Their marketing research department chose a particular football stadiumt to test market a new jumbo hot dog. It was found that the demand for the new hot dog is given approximately by

 

p=6-ln(x), 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?

 

Price = __________

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Expert Answer

Step 1

Given information

Total no. of hot dog sold is x thousands

New hot dog is approximately

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Step 2

Calculation:

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Step 3

For maximum profit take first derivation of P ...

dP
d
(5x-xlnx)
dx
dx
dP d(5x) d
(xInx)
dx
dx
dx
dP
= 5-1
dx
-In x
х
dP
= 5-1-nx 4- Inx
dP
for max take
dx
0 =
hence, 4-nx 0
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dP d (5x-xlnx) dx dx dP d(5x) d (xInx) dx dx dx dP = 5-1 dx -In x х dP = 5-1-nx 4- Inx dP for max take dx 0 = hence, 4-nx 0

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Math

Calculus

Derivative

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