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Poppy produces bead necklaces. The material for each necklace costs $4. She has been selling them for $8 each and averages sales of 40 necklaces per week. If she increases the price by $0.50, she would lose 4 sales each week. What should be the selling price to maximize her profit.

 Feb 11, 2021
 #1
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Sorry, for some reason the question got messed up:

 

Poppy produces bead necklaces. The material for each necklace costs 4 dollars. She has been selling them for $8 each and averages sales of 40 necklaces per week. If she increases the price by $0.50, she would lose 4 sales per week. What should be the selling price to maximize her profit.

 Feb 11, 2021
 #2
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Let  x   be  the  number of  .50   increases

 

Note  that  she really only makes    ( $8 -$4) =  $4  on the sale of each bracelet

 

So

 

Profit  =  Sales Price  *   Units sold

 

Profit  =    ( 4 + .50x)  ( 40  - 4x)

 

P =  160  +  20x - 16x - 2x^2        rearrange  as

 

P  = -2x^2   +  4x   +  160

 

The  number of .50   increases  that max  the profit  =    -4 / ( 2 (-2))  =    4/4 =   1

 

So......the selling  price  that would max  the profit  =  8 + .50    =   $8.50

 

cool cool cool

 Feb 11, 2021
edited by CPhill  Feb 11, 2021

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