SOLUTION: the cost in millions of dollars for a company to manufacture x thousand automobiles is given by the function C(x)=5x^2-20x+36. find the number of automobiles that must be produced

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Question 917382: the cost in millions of dollars for a company to manufacture x thousand automobiles is given by the function C(x)=5x^2-20x+36. find the number of automobiles that must be produced to minimize the cost.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
C(x)=5x^2-20x+36. find the number of automobiles that must be produced to minimize the cost.
C%28x%29=5x%5E2-20x%2B36+ ...this is a parabola opening upward, completing the square to find the
vertex
C%28x%29=5x%5E2-20x%2B36+ .........write 36 as 20%2B16
c%28x%29=+5x%5E2-20x%2B20%2B16 ...group
C%28x%29=+%285x%5E2-20x%2B20%29%2B16
C%28x%29=+5+%28x%5E2-4x%2B4%29%2B16
C%28x%29=+5+%28x-2%29%5E2%2B16


Vertex(2,16) => x=+2 OR 2000 automobiles