SOLUTION: The total cost of producing a type of car is given by C(x)=23000−30x+0.04x^2, where x is the number of cars produced. How many cars should be produced to incur minimum cost?

Question 1149669: The total cost of producing a type of car is given by C(x)=23000−30x+0.04x^2, where x is the number of cars produced. How many cars should be produced to incur minimum cost?
Answer by ikleyn(52858) (Show Source): You can put this solution on YOUR website!
.


You are given a quadratic function  C(x) = 23000 - 30x + 0.04x^2.



Any quadratic function y = ax^2 + bx + c  with positive leading coefficient at x^2 has the minimum at the value of 


    x = .


In your case  a= 0.04  and  b= 30. Hence, the given quadratic function gets the minimum at


    x =  = 375.


ANSWER.  375 cars should be produced to get minimum cost.

Solved.

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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
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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