Question 1209304
.
The Art of Problem Solving has begun selling a cookbook called "What Would Euler Eat?"  
If the price of the cookbook is n dollars (n <= 10), then it will sell 100 - 10n copies.  
What price per book (in dollars) will maximize the total revenue we receive for all the books sold?
~~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
At n <= 10, the total revenue is

    R(n) = n*(10-n) = 10n - n^2.


This formula represent a downward parabola, so it has a maximum.


The maximum/(the vertex) is at  n = {{{-b/(2a)}}}, where "a" is the coefficient at n^2, 
"b" is the coefficient at n

      {{{n[max]}}} = = {{{-10/(2*(-1))}}} = 5.


The revenue is maximum at n= 5 dollars.    <U>ANSWER</U>
</pre>

Solved.


---------------------


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.