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A tour company has a ticket price that goes down $2 for every additional person who signs up for a group trip. They charge, per person, 52-2n Where n is the number of people that go on the trip. Their total revenue, R, as a function of the number of people who can go in the trip is R=52n-2n^2. How many people Maximize the revenue for the tour company

Respuesta :

Answer:

13 people will Maximize the revenue for the tour company

Step-by-step explanation:

Data provided in the question:

Revenue function = 52n - 2n²

Now,

To find the point of maxima or minima, differentiating the revenue funtion with respect to the 'n' and equating to zero

⇒ [tex]\frac{dR}{dn}=\frac{d(52n-2n^2)}{dn}[/tex] = 0

or

⇒ 52 - 4n = 0

or

⇒ 4n = 52

or

⇒ n = 13

To check for mamixa or minima

again differentiating the revenue function

i.e

[tex]\frac{d^2R}{dn^2}[/tex] = -4     [negative value means the n = 13 is point of maxima ]

Hence,

13 people will Maximize the revenue for the tour company

13 people will maximize the revenue for the tour company.

    Function defining the total Revenue 'R' generated is,

  • R = 52n - 2n²

Here, n = Number of people going on the trip

For maximum revenue,

"Find the derivative of the function with respect to 'n' and equate it to zero to find the value of n"

[tex]\frac{d}{dn}(R)=\frac{d}{dn}(52n-2n^2)[/tex]

R' = 52 - 4n

Find double derivative of the function R.

R" = -4

Since, its negative so the revenue will be maximum.

For R' = 0

52 - 4n = 0

n = 13

     Therefore, revenue will be maximum for 13 people.

Learn more,

https://brainly.com/question/23417263

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