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.

Question

Write an equation to express the revenue, R(x) dollars, in terms of a price increase of x dollars

Find the coordinates of the maximum point of this function

What admission cost gives the maximum revenue?

How many visitors give the maximum revenue?

Answer 1

R(x) = (8+x)(2000-100x)
So, that is just a parabola, with its vertex (maximum revenue) at x=6

Now you can answer the other questions.

Answer 2

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Answer 3

y=4x+8

Answer 4

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