Question 1116065: A movie theater is considering lowering ticket prices. If it lowers ticket prices by x dollars,
the expected revenue function per week is r(x)=-500(x-2.5)^+28,025. What decrease in
ticket prices will produce the maximum revenue for the theater? What is the maximum
revenue that is possible?
Thanks for your help.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! The revenue function is
 .
When you do not remember "formulas"
and other calculation tricks and problem-solving recipes taught in class,
using your own brain may work, if a little slower.
You do not need to have been awake during the classes about quadratic functions to know that
 no matter what real number value  and  take;
 no matter what, and as a consequence
 no matter what.
You should also realize that the only way to have 
is to have  ,
which means  ,
 , and  .
So, if (and only if)
the movie theater lowers ticket prices by  dollars,
they can expect the maximum predicted revenue of  .
NOTE: Quadratic functions graph as parabolas,
with a maximum (if the coefficient of the squared term is negative),
or a minimum (if that coefficient is positive).
They can be found in the form
 or  ,
Where a,b,c,h, and k are constants,
but it must be  (or it is not a quadratic function).
You can also find them in any other equivalent form that your teacher could choose.
It will be up to you to recognize what you are dealing with.
If your teacher is merciful, the function will look like ,
and as explained at the top  will be
the value where the maximum or minimum happens,
and that maximum or minimum value of the function will be  .
If the quadratic function appears in the form ,
you could transform it to the equivalent, but more useful form,
or you could remember that the maximum or minimum happens for' .
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