SOLUTION: Suppose that the price per unit in dollars of a cell phone production is modeled by p = $85 − 0.0125x, where x is in thousands of phones produced, and the revenue represente

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Question 1127680: Suppose that the price per unit in dollars of a cell phone production is modeled by p = $85 − 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.

Found 3 solutions by addingup, Cityscape16, ikleyn:
Answer by addingup(3677)   (Show Source): You can put this solution on YOUR website!
R Revenue
p: price
q: quantity
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
R(q) = p * q
R(q) =

Answer by Cityscape16(2)   (Show Source): You can put this solution on YOUR website!
85-0.0125x = 85/0.0125 = 3400 production level

Answer by ikleyn(52767)   (Show Source): You can put this solution on YOUR website!
.
From the condition, the revenue is


    R(x) = x*p = x*(85-0.o0125x) = -0.00125 + 85x   thousands of dollars.


It is a quadratic function, and the problem asks you to find its maximum.


For the general form quadratic function  y(x) = ax^2 + bx + c  with the negative leading coefficient "a" 
the maximum is achieved at  x = .


In our case,  a = 0.0125,  b= 85,  so the maximum is achieved at 

    x =  =  6800.


It is "the production level that will maximize revenue".   ANSWER

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On finding the maximum/minimum of a quadratic function see the lessons
    - HOW TO complete the square to find the minimum/maximum of a quadratic function
    - Briefly on finding the minimum/maximum of a quadratic function
    - HOW TO complete the square to find the vertex of a parabola
    - Briefly on finding the vertex of a parabola

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

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


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.


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