Question 1058958
.
A manufacturer of microwave ovens believes that the revenue R, in dollars, that the company receives is related to 
the price P, in dollars, of an oven by the function R(P) = 85P – 0.25P^2. What price will give the maximum revenue?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
They want you find the maximum of this quadratic function

R(P) = {{{85P - 0.25P^2}}}.

The general theory says that the quadratic function y(x) = {{{ax^2 + bx + c}}} has the maximum/minimum at x = {{{-b/2a}}},

which in your case is {{{-85/(2*(-0.25))}}} = {{{-85/(-0.5)}}} = 170 dollars.

<U>Answer</U>.  170 dollars.
</pre>

There is a bunch of lessons in this site on finding the maximum/minimum of quadratic functions

&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>