SOLUTION: A manufacturer of lighting fixtures has daily production costs of C = 800 - 30x + 0.75x^2, where C is the total cost (in dollars) and x is the number of units produced. How m

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Question 1118640: A manufacturer of lighting fixtures has daily production costs of
C = 800 - 30x + 0.75x^2, where C is the total cost (in dollars) and x is the number of units produced.
How many fixtures should be produced each day to yield a minimum cost?

Answer by ikleyn(52863)   (Show Source): You can put this solution on YOUR website!
.
To solve the problem, you need to find the maximum of the quadratic function 


C(x) = .


The maximum of the quadratic function


q(x) = 


with positive coefficient "a" is achieved at  x = .


In your case  b = -30,  a = 0.75,  therefore the maximum is achieved at


x =  =  = 40.


Answer.  40 fixture per day provide minimum cost.

Solved.

--------------------
On finding 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
in this site.

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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