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A shoe store sells about 200 pairs of a new basketball shoe each month when it charges $60 per pair. For each $1 increase in price, about 2 fewer pairs per month are sold. How much per pair should the store charge to maximize monthly revenue? What is the maximum revenue?

 Jan 26, 2020
 #1
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Increase price 1   2 fewer pairs sold

   for 'x' dollar increase:

       Price         *     pairs sold                         = revenue

     (60 +  x)      *      (200-2x)                          = revenue

         12000 -120x + 200x -2x^2                     = revenue

                        -2x^2+80x+12000                   = revenue       This will be an upside down parabola  (due to the -2x^2)

 

Maximum will be at   -b/2a       a = -2   b = 80

 

                               80/4 = $ 20     this is the mumber of 1 $ increases.....so   $80 per pair will maximize profit

 

Plug in that price    x       pairs sold 

         $80                x        ( 200 - 2(20))     =    max revenue

 Jan 27, 2020

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