Question 1209141
.
Carly just opened her own nail salon. Based on experience, she knows that her daily profit, P, 
in dollars, can be modelled by the relation P=-15x^2+240x-640, where x is number of clients 
per day. How many clients should she book each day to maximize her profit?
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<pre>
The given function is a quadratic function.

Since the coefficient at x^2 is negative, the parabola is downward and has a maximum.


The maximum value is achieved  a  {{{c[max]}}} = {{{-b/(2a)}}},  where "a" is the coefficient at x^2

and "b" is the coefficient at x.  In your case,


    {{{x[max]}}} = {{{-240/(-2*(-15))}}} = {{{240/30}}} = 8.


Hence, the profit is maximum if Carly books 8 clients per day.    <U>ANSWER</U>
</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.