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.

Guest Feb 11, 2021

#1**0 **

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.

Guest Feb 11, 2021

#2**+1 **

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

CPhill Feb 11, 2021