Answer:
Minimum cost is $12427.85
Step-by-step explanation:
The unit cost C is given as:
[tex]C(x)=0.3x^2-66x+14,571[/tex] where x is the number of cars made.
To determine the minimum cost, C(x), first we determine the minimum value of the quadratic expression [tex]0.3x^2-66x+14,571[/tex]
When a>0, C(x) will attain minimum value at the point determined by [tex]x=-\dfrac{b}{2a}[/tex].
Comparing [tex]0.3x^2-66x+14,571[/tex] with the general form of a quadratic expression [tex]ax^2+bx+c[/tex]
a=0.3, b=-66, c=14571
Minimum Value occurs at [tex]x=-\dfrac{b}{2a}=-\dfrac{-66}{2X0.3}=\dfrac{66}{0.6}=39.6[/tex]
Therefore, the Minimum Cost, C(x) occurs at the point x=39.6
Substituting x=39.6 into C(x)
C(39.6)=[tex]0.3(39.6)^2-66(39.6)+14571=12427.85[/tex]
The Minimum cost is $12427.85
