SOLUTION: The cost in millins 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

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The cost in millins 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      Log On


   

Question 294733: The cost in millins 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

Tried to factor out the four then simpliy. Stuck. Help!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The minimum is the C(x) value that is the smallest (ie it is the smallest cost value). This minimum occurs at the vertex (h,k) where

h=-b%2F2a

In this case, b=-16 and a=4 meaning that h=-%28-16%29%2F%282%284%29%29=16%2F8=2. In other words, if 2 thousand autos are produced, then the cost will be at a minimum. Simply plug this value into the function to get:

C%282%29=4%282%29%5E2-16%282%29%2B32=4%284%29-16%282%29%2B32=16-32%2B32=16 which means that C%282%29=16. So the minimum cost is 16 million dollars (when 2 thousand autos are manufactured).


So the vertex is the point (2,16). What this means is that if we graph C%28x%29=+4x%5E2-16x%2B32, the lowest point on the graph is (2,16)