Question 630441: The cost in millions of dollars for a company to manufacture x thousand automobiles is given by the function C(x)=3x2-30x+175. Find the number of automobiles that must be produced to minimize the cost.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! The cost in millions of dollars for a company to manufacture x thousand automobiles is given by the function C(x)=3x2-30x+175. Find the number of automobiles that must be produced to minimize the cost.
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C(x)=3x2-30x+175
This is an equation of a parabola that opens upwards (curve has a minimum)
Its standard form: (x-h)^2+k, (h,k)=(x,y) coordinates of the vertex.
complete he square:
C(x)=3(x2-10x+25)+175-75
C(x)=3(x-5)^2+100
vertex:(5,100)
number of automobiles that must be produced to minimize the cost=5 thousand
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