SOLUTION: Suppose that the cost function for the production of a particular item is given by the equation C(x)=5x^2-400x+12,920 where x represents the number of items. How many items should

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Question 577035: Suppose that the cost function for the production of a particular item is given by the equation C(x)=5x^2-400x+12,920 where x represents the number of items. How many items should be produced to minimize the cost?
Answer by htmentor(1343) About Me  (Show Source):
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Suppose that the cost function for the production of a particular item is given by the equation C(x)=5x^2-400x+12,920 where x represents the number of items. How many items should be produced to minimize the cost?
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C(x)=5x^2-400x+12,920
The cost will be minimized when dC/dx = 0
dC/dx = 10x - 400 = 0
This gives x = 40
We can also see this from the graph of the cost function:
graph%28300%2C300%2C-10%2C60%2C-500%2C13000%2C5x%5E2-400x%2B12920%29