SOLUTION: The cost in millions of dollars for a company to manufacture x thousand automobiles is given by the function C(x)=3x^2 - 24x + 144. Find the number of automobiles that must be prod

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Question 536414: The cost in millions of dollars for a company to manufacture x thousand automobiles is given by the function C(x)=3x^2 - 24x + 144. Find the number of automobiles that must be produced to minimize the cost
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+C%28x%29+=+3x%5E2+-+24x+%2B+144+
Set equal to zero to locate roots
The minimum will be exactly
midway between the 2 roots
++3x%5E2+-+24x+%2B+144+=+0+
Divide both sides by 3
+x%5E2+-+8x+%2B+48+=+0+
This is in the form
+ax%5E2+%2B+b%2Ax+%2B+c+
The x value at the minimum will be at +-b%2F%282a%29+
+x%5Bmin%5D+=+-%28-8%29%2F%282%2A1%29+
+x%5Bmin%5D+=+4+
4 thousand produced will minimize cost, C(x)
here's a plot:
+graph%28+400%2C+400%2C+-2%2C+10%2C+-10%2C+80%2C+x%5E2+-+8x+%2B+48+%29+