web2.0calc
 
+0  
 

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

0
2021
2
avatar+142 

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

2+0 Answers

 #1
avatar+6248 
+2

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

.
 Jul 28, 2019
 #2
avatar+142 
+3

Thank you :)

 Jul 28, 2019

1 Online Users

avatar

Top Users

avatar+128475 CPhill moderator
avatar+118609 Melody moderator
avatar+33616 Alan moderator
avatar+14917 asinus moderator
avatar+9519 MaxWong
avatar+3144 admin administrator
avatar+2440 GingerAle
avatar+1791 tomtom
avatar+1509 bader
avatar+1105 parmen
avatar+1032 kittykat

Sticky Topics