Question 1203125
.
Brooklyn has a summer window washing business. Based on experience 
Brooklyn knows that P= - 2x² + 130x - 1500 models her profit, P, in dollars, 
where x is the amount she charges per window. 
(a) How much must Brooklyn charge to maximize her profit? 
(b) What is the maximum profit?
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<pre>
They want you find the maximum of the quadratic function P(x) = -2x^2 + 130x - 1500.


It is well known fact that a quadratic function f(x) = ax^2 + bx + c gets its maximum value at  

              {{{x[max]}}} = {{{-b/(2a)}}}.


In your case,  a= -2, b= 130,  therefore,  {{{x[max]}}} = {{{-130/(2*(-2))}}} = {{{130/4}}} = 32.50 dollars.


The maximum profit is then  P(32.50) = -2*32.50^2 + 130*32.50 - 1500 = 612.50 dollars.


<U>ANSWER</U>.  (a) $32.50;  (b) $612.50.
</pre>

Solved.


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On finding the maximum/minimum of a quadratic function see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/HOW-TO-complete-the-square-of-a-quadratic-function-to-find-its-minimum-maximum.lesson>HOW TO complete the square to find the minimum/maximum of a quadratic function</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Briefly-on-How-to-complete-the-square-of-a-quadratic-function-to-find-its-minimum-maximum.lesson>Briefly on finding the minimum/maximum of a quadratic function</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/HOW-TO-complete-the-square-to-find-the-vertex-of-a-quadratic-function.lesson>HOW TO complete the square to find the vertex of a parabola</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Briefly-on-finding-the-vertex-of-a-parabola.lesson>Briefly on finding the vertex of a parabola</A>


Consider these lessons as your textbook, &nbsp;handbook, &nbsp;tutorials and &nbsp;(free of charge) &nbsp;home teacher.

Learn the subject from there once and for all.