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# Poppy

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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

### 2+0 Answers

#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

Feb 11, 2021
edited by CPhill  Feb 11, 2021