Question 1204337
.
A company finds that it can make a profit of P dollars each month by selling
x patterns, according to the formula
P(x)=-.002x^2+5.5x-1400. How many patterns must it sell each month to have a maximum profit? 
To attain maximum profit they must sell
patterns.

What is the maximum profit? 
The max profit is $
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<pre>
They want you find the maximum of the quadratic function  P(x) = ax^2 + bx + c = -0.002x^2 + 5.5x - 1400.


The general theory says that the maximum is attained at  {{{x[max]}}} = {{{-b/(2a)}}} = {{{-5.5/(2*(-0.002))}}} = {{{5.5/0.004}}} = 1375.


To get the value of the maximum profit, substitute this value {{{x[max]}}} = 1375 into the formula for the profit.
You will get

    {{{P[max]}}} = -0.002*1375^2 + 5.5*1375 - 1400 = 2381.25  dollars.


<U>ANSWER</U>.  {{{x[max]}}} = 1375 patterns.

         {{{P[max]}}} = 2381.25  dollars.
</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>



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