Question 1071427
.
Suppose that the price per unit in dollars of a cell phone production is modeled by p = $35 − 0.0125x,
where x is in thousands of phones produced, and the revenue represented by thousands of dollars is R = x · p.
Find the production level that will maximize revenue. 
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<pre>
According to the condition, the revenue (measured in thousands of dollars) is 

R(x) = x*(35-0.0125x),

where x is the number of the phones measured in thousand of units.

So, you need to find the maximum of this quadratic function

R(x) = -0.0125x^2 + 35x.

The maximum is achieved at x = {{{-b/(2a)}}}  ( referring to the general form of a quadratic function q(x) = {{{ax^2 + bx + c}}} ),

which at given conditions is x = {{{-35/(2*(-0.0125))}}} = {{{35/0.025}}} = 1400.

So, the maximum is achieved at the production level 1400 thousand of phone units .

The maximum revenue is the value R(x) at this value of x:

{{{R[max]}}} = R(1400) = {{{-0.0125*1400^2 + 35*1400}}} = 24500 thousands of dollars.

<U>Answer</U>.  The maximum revenue is 24500 thousands of dollars achieved at the production level of 1400 thousand of phone units .
</pre>

Solved.


To see other similar solved problems, see the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/Using-quadratic-functions-to-solve-problems-on-maximizing-profit.lesson>Using quadratic functions to solve problems on maximizing revenue/profit</A>

in this site.


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>



Also, you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this textbook under the topic "<U>Finding minimum/maximum of quadratic functions</U>".