SOLUTION: The cost in millions of dollars for a company to manufacture x thousand automobiles is given by the function C(x)=4x^2-24x+81. Find the number of autromobiles that must be produced
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-> SOLUTION: The cost in millions of dollars for a company to manufacture x thousand automobiles is given by the function C(x)=4x^2-24x+81. Find the number of autromobiles that must be produced
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Question 427096: The cost in millions of dollars for a company to manufacture x thousand automobiles is given by the function C(x)=4x^2-24x+81. Find the number of autromobiles that must be produced to minimize cost.
Answer key states 3,000. Found 2 solutions by ewatrrr, htmentor:Answer by ewatrrr(24785) (Show Source):
Hi
The cost in millions of dollars for a company to manufacture x thousand
automobiles is given by the function C(x)=4x^2-24x+81.
Find the number of autromobiles that must be produced to minimize cost.
4x^2-24x+81 |parabola opening upward. completing the square to find the vertex
c(x)= 4[(x-3)^2 -9] + 81
c(x)= 4(x-3)^2 - 36 + 81
c(x)= 4(x-3)^2 + 45 Vertex(3,45) x= 3 OR 3000 automobiles
You can put this solution on YOUR website!
This function will have a minimum where dC(x)/dx = 0
Taking the derivative, and setting = 0, we have
Solving for x gives, x = 3
So the answer is 3000 automobiles
Here is the graph of the function:
