SOLUTION: The unit cost in dollars for manufacturing IPODS is given by C(n)=0.004n^2-3.2n +660. what is the minimum cost?

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Question 691424: The unit cost in dollars for manufacturing IPODS is given by C(n)=0.004n^2-3.2n +660. what is the minimum cost?
Answer by mouk(232) About Me  (Show Source):
You can put this solution on YOUR website!
Let +C=0.004n%5E2-3.2n+%2B660+
then +dC%2Fdn+=+%282%29%280.004n%5E1%29+-+3.2+=+0.008n+-+3.2+
Critical values occur when +dC%2Fdn+=+0+
so, +0.008n+-+3.2+=+0+
+0.008n+=+3.2+
+n+=+3.2%2F0.008+=+400+
Does +n+=+400+ correspond to a max or min?
Look at the second derivative:
+dC%2Fdn+=+0.008n+-+3.2+ so then +d%5E2C%2Fdn%5E2+=+0.008+
which is +ve so critical point is a MINIMUM
Hence, minimum cost occurs when +n+=+400+ so minimum cost is found by putting +n+=+400+ in original equation
Giving minimum cost = 20