Probem56+Elana+Kevin+Susie

Kevin Wu: (a) Find the demand function, assuming that it is linear. (b) If the material for each necklace costs Terry $6, what should the selling price be to maximize his profit?
 * 1) 56. During the summer months Terry makes and sells necklaces on the beach. Last summer he sold the necklaces for $10 each and his sales averaged 20 per day. When he increased the price by $1, he found that the average decreased by two sales per day.

(a) D=demand (sales per day); C=cost of necklaces (10,20) (11,18) D=mC+b m=2/-1=-2 20=-2(10)+b b=40 D=-2C+40

(b) P=profit Profit=(cost of necklace)(demand)-(cost to make) P=C(-2C+40)-6 P=-2C^2+40C-6 Maximize this by finding critical points by taking first derivative and setting it equal to zero. P'=-4C+40 0=-4C+40 -40=-4C C=10 Therefore, in order to maximize his profit, Terry should set the cost of the necklace to $10.

consider the endpoints! What is the fewest number of necklaces Terry will make? waht ist he maximum?

Lim P : -6 x -> 0

Lim P : -infinity x-> infinity

Lim P: 194 Therefore when X = 10 this is the maximum profit he can receive. x -> 10