Question

The unit cost C depends on the number of cars made. If x cars were made, then the unit cost is given by the function C(x)=0.3x^2-66x+14,571. What is the minimum cost?

Answer 1

Minimum cost is $12427.85

Explanation:

The unit cost C is given as:

`C(x)=0.3x^2-66x+14,571` 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
`0.3x^2-66x+14,571`

When a>0, C(x) will attain minimum value at the point determined by
`x=-(b)/(2a)`.

Comparing
`0.3x^2-66x+14,571` with the general form of a quadratic expression
`ax^2+bx+c`

a=0.3, b=-66, c=14571

Minimum Value occurs at
`x=-(b)/(2a)=-(-66)/(2X0.3)=(66)/(0.6)=39.6`

Therefore, the Minimum Cost, C(x) occurs at the point x=39.6

Substituting x=39.6 into C(x)

C(39.6)=
`0.3(39.6)^2-66(39.6)+14571=12427.85`

The Minimum cost is $12427.85