demand function & maximize profit

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chica2006

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Apr 11, 2006
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Hi I need help with the following problem:

during the summer months mary makes and sells bracelets. last summer she sold the necklaces for $10 each and her sales averaged 20 per day. When she increased the price by $1, she found she lost 2 sales per day.

a) find the demand function, assuming that it is linear

b) if the material for each necklace cost mary $4, what should the selling price be to maximize her profit?

*show work

thanks :)
 
This is what I have so far for the answer. IS this right?

a) y= 10; x=20

m = 20 -18/10-11
m = -2/-1
m = 2

p(x) = -2x + 10
D(p) = -2(p) + 10 or 10 -2p
D'(p) = -2

b) R(p) = pD(p)
R(p) = p(10 - 2p)
=10p - 2p²
R'(p)= 10-4p
10-4p=0
-4p=-10
p=-10/-4 or 2.5
R''= -4 so it is maximum
2.5 + 4 = 6.5

should sell at $6.50
 
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