SOLUTION: A bottle manufacturer has a daily production cost of C=1600-10x+0.25x2. How many bottles should be produced each day to have a minimum cost?

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Question 1196018: A bottle manufacturer has a daily production cost of C=1600-10x+0.25x2. How many bottles should be produced each day to have a minimum cost?
Answer by ikleyn(52780)   (Show Source): You can put this solution on YOUR website!
.
A bottle manufacturer has a daily production cost of C=1600-10x+0.25x2.
How many bottles should be produced each day to have a minimum cost?
~~~~~~~~~~~~~

They want you find the minimum of the quadratic function C(x) = 1600 - 10x + 0.25x^2.


The minimum is achieved at x = , where "a" is the coefficient
at the quadratic term x^2 and "b" is the coefficient at the linear term.


In your case, a = 0.25,  b= -10, therefore

     =  =  =  = 20.


ANSWER.  20 bottles should be produced each day.

Solved.

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

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


Consider these lessons as your textbook,  handbook,  tutorials and  (free of charge)  home teacher.
Learn the subject from there once and for all.


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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