SOLUTION: An amusement park has been charging $12 per person for admission and averaging 1000 patrons per day. the directors of the park are considering a $2 increase in the price for next s

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Question 446766: An amusement park has been charging $12 per person for admission and averaging 1000 patrons per day. the directors of the park are considering a $2 increase in the price for next season . They have calculated that for each $2 in increase they will probably lose 100 patrons per day. What should be the ideal admission fee for the greatest income on an average day . Write an equation to model the situation and draw a graph of the situation to justify your answer.
So I got the ideal price to be $16
The equation is what i'm not sure of , I got (x-16)^2= p(y-12800) Not sure on how to find P , Also not sure if the equation is correct
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
An amusement park has been charging $12 per person for admission and averaging 1000 patrons per day.
the directors of the park are considering a $2 increase in the price for next season .
They have calculated that for each $2 in increase they will probably lose 100 patrons per day.
What should be the ideal admission fee for the greatest income on an average day
. Write an equation to model the situation and draw a graph of the situation to justify your answer.
:
I think you are right, but I would do it this way.
:
Let x = no. of $2 increases and no. of 100 patron decreases
:
Income = price * no. patrons
f(x) = (12+2x)*(1000-100x)
Foil
f(x) = 12000 - 1200x + 2000x - 200x^2
A quadratic equation
f(x) = -200x^2 + 800x + 12000, is the equation
:
The greatest income occurs when x = the axis of symmetry, x = -b/(2a)
x = %28-800%29%2F%282%2A-200%29
x = +2
Therefore max income when
12+2(2) = $16 is the price (which you got)
then
1000 - 2(100) = 800 patrons at that price
Max income
16 * 800 = $12,800
:
To graph this
+graph%28+300%2C+200%2C+-4%2C+8%2C+-2000%2C+18000%2C+-200x%5E2%2B800x%2B12000%29+
:
You can confirm this, substitute 2 in the equation to find f(x) = 12,800