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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?

 

Please help me. Thanks in advance! smiley

 Jul 14, 2019
 #1
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Price of phone = 450 - 5x      where x = number of $5 decreases in price

    income from number of phones sold will be   500(450-5x)  + 10x (450-5x)

                                                                                 225000 - 2500x + 4500x - 50 x^2

                                                                                 - 50 x^2  + 2000x + 225000     = revenue

          Max occurs at - b/2a  =  -2000/(2*-50) = 20 reductions of $5

                  $350 price results in maximum revenue of $ 245000

 Jul 14, 2019
 #2
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Thank you!!!laugh

 Jul 14, 2019
 #3
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You are welcome..... I hope you understand the solution!   ~EP

ElectricPavlov  Jul 14, 2019

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