SOLUTION: A vehicle factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made. If x cars are made, then the unit cost is given by t

Question 1062690: A vehicle factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made. If x cars are made, then the unit cost is given by the function
c(x)=1.2x^2-384x+38,667
What is the minimum unit cost?
Answer by ikleyn(52784) (Show Source): You can put this solution on YOUR website!
.
A vehicle factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made.
If x cars are made, then the unit cost is given by the function
c(x) = 1.2x^2 - 384x + 38,667
What is the minimum unit cost?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

If you are given a quadratic function 

    y = ax^2 + bx + x      (1)

(with the positive coefficient "a", as it is in your case), then it achieves the minimum at 

    x = .             (2)


In your case this value of x is x =  = 160.


Now to find the minimal value of the quadratic function (1), you simply need to substitute the value (2) into the function.

In your case, you need to substitute the value x = 160 to get the minimum unit cost

    = 1.2*160^2 - 384*160 + 38,667.


Please make this calculation on your own.

There is a bunch of lessons in this site on finding the maximum/minimum of a quadratic function
    - 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
    - A rectangle with a given perimeter which has the maximal area is a square
    - A farmer planning to fence a rectangular garden to enclose the maximal area
    - A farmer planning to fence a rectangular area along the river to enclose the maximal area
    - A rancher planning to fence two adjacent rectangular corrals to enclose the maximal area
    - Using quadratic functions to solve problems on maximizing revenue/profit
    - OVERVIEW of lessons on finding the maximum/minimum of a quadratic function

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".

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