# HELP

#### chica2006

##### New member
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? 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

#### jacket81

##### Junior Member
Okay, I could be wrong, but this is what I have on b:

(10+p-4)(20-2p) =
(6+p)(20-2p) =

120-12p+20p-2p^2 = 120+8p-2p^2

So, differienate and set to 0:

8-4p=0, so
8=4p

So, p=2.

So, set price at 10+2=12?