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anonymous
 5 years ago
An amusement park charges $8 admission and average of 2000 visitors per day. A survey shows that for each $1 increase in the admission cost, 100 fewer people would visit the park.
a) Write an equation to express the revenue, R(x) dollars, in terms of a price increase of x dollars
b) Find the coordinates of the maximum point of this function
c) What admission cost gives the maximum revenue?
d) How many visitors give the maximum revenue
anonymous
 5 years ago
An amusement park charges $8 admission and average of 2000 visitors per day. A survey shows that for each $1 increase in the admission cost, 100 fewer people would visit the park. a) Write an equation to express the revenue, R(x) dollars, in terms of a price increase of x dollars b) Find the coordinates of the maximum point of this function c) What admission cost gives the maximum revenue? d) How many visitors give the maximum revenue

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You need to find the revenue, R(x), which is by definition, R(x) = (admission per person) x (number of people) We know that if we increase the admission per person by 1 unit, the number of people goes down 1 unit, so R(x) = (8 + 1)*(2000  100) If we define the variable 'x' to represent the number of increases in price, from what we've begun to establish, \[R(x)=(8+x)(2000100x)\]Expanding gives, \[R(x)=16000+1200x200x^2\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The maximum point will be given for\[R'(x)=1200200x\]Setting R'(x) to zero and solving gives,\[x=6\]The corresponding Rcoordinate is then, \[R(6)=19600\]The coordinate of the maximum is therefore (6,19600).

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The park should make a 6unit increase to maximize its revenue. So the admission cost should be $14. The number of people attending would then by 19,600.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thanks so much for your help!
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