SOLUTION: Solve the problem. The cost in millions of dollars for a company to manufacture x thousand automobiles is given by the function C(x) = 5x^2

SOLUTION: Solve the problem. The cost in millions of dollars for a company to manufacture x thousand automobiles is given by the function C(x) = 5x^2 - 50x + 225. Find the number of autom

Question 765271: Solve the problem.
The cost in millions of dollars for a company to manufacture x thousand automobiles is given by the function C(x) = 5x^2 - 50x + 225. Find the number of automobiles that must be produced to minimize the cost.

Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Solve the problem.
The cost in millions of dollars for a company to manufacture x thousand automobiles is given by the function C(x) = 5x^2 - 50x + 225. Find the number of automobiles that must be produced to minimize the cost.
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Minimum occurs when x = -b/(2a) = 50/(2*5) = 5
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Cheers,
Stan H.
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
The minimum is the value that is the lowest point on a graph which is a parabola that opens up, so minimum occurs at the vertex (,) where

given:

so, and
meaning that
In other words, if thousand autos are produced, then the cost will be at a .
Simply plug this value into the function to get:

So the minimum cost is million dollars when thousand autos are manufactured).

So the vertex is the point (,). What this means is that if we graph , the lowest point on the graph is (,).

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