+0

# A shop sells 500 smartphones a week for $450 each... 0 266 2 +140 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

#1
+6046
+2

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

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Jul 28, 2019
#2
+140
+3

Thank you :)

Jul 28, 2019