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 A shop sells 500 smartphones a week for $450 each...

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A shop sells 500 smartphones a week for $450 each. A market survey shows that each decrease of $5 on the price will result in the sale of an additional 10 smartphones per week. What price of the smartphone would result in maximum revenue, in dollars?

 Jul 28, 2019

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 #1
avatar+6251 
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\(R(p) = N(p) p\\ p = 450-5k\\ N(p) = 500+10k\\ R(p) = (500+10k)(450-5k) = \\ -50 k^2+2000 k+225000 = \\ -50(k^2-40k - 4500) = \\ -50((k-20)^2 - 400-4500) = \\ -50((k-20)^2-4900) = \\ -50(k-20)^2 + 245000\\~\\ \text{The maximum is at $k=20$, i.e. a price of \$350}\)

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 Jul 28, 2019
 #2
avatar+142 
+3

Thank you :)

 Jul 28, 2019

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