Question

The cost in millions of dollars for a company to manufacture x thousand automobiles is given by the function C(x)=4x^(2)-16x+32. Find the number of automobiles that must be produced to minimize the cost, then find the minimum cost to the nearest dollar.

Answer 1

Minimum point at:
x = - 4/2 = 2 auto
=> C (2) = 4 ( x² - 4x + 8 ) = $16
Thus 2,000 automobiles must be produced to minimize the cost to 16 billions dollars.

Answer 2

should it be 16 million instead of 16 billion? Can you show me the steps in how you got the answer?

Answer 3

Oop, I guess I feel sleepy already :P

Answer 4

Any way the formula to find minimum point is x = - b/2a
That's all I do!

Answer 5

so if you use -b/2a, then i guess the 4 from 4x^(2), but what about the 2a? what number do we plug in place of the a?

Answer 6

the quadratic function\[f(x)=ax^{2}+bx+c\]the vertex\[x=\frac{-b}{2a}\]

Answer 7

the original equation is 4x^(2)-16x+32, so is the vertex -16/2(4)?

Answer 8

I need to show the step in getting the answers. Can you please show me?

Answer 9

because\[a>0\]the vertex is the minimum. actually the vertex is a point, and this is the x value.\[x=\frac{-b}{2a}=\frac{-(-16)}{2(4)}=2\]to minimize the cost, we need to produce 2 thousand automobiles\[C \left( 2 \right)=4(2)^{2}-16(2)+32\]\[C(2)=16\]and the minimum cost is $16 million dollars

Answer 10

thank you very much, have time for one more?

Answer 11

I'll just post it for all