   SEARCH HOME Math Central Quandaries & Queries  Question from apoorva, a student: 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 he lost two sales per day. a. Find the demand function, assuming it is linear. b. If the material for each necklace costs Terry $6, what should the selling price be to maximize his profit? Apoorva, The demand function is the price p(x) per necklace Terry can charge and if he sells x necklaces. If this is a linear function then p(x) = ax + b where a and b are constants. Last summer when the price was$10 he sold 20 necklaces per day so

$10 = p(20) = 20 a + b When he increased the price to$10 + $1 =$11 he lost 2 sales per day. Thus

\$11 = p(18) = 18 a + b

Solve these equations for a and b.

The revenue that Terry makes is R(x)= x × p(x) and his cost is C(x) = 6 x Write an expression for the profit he makes and use your knowledge of calculus to maximize the profit.

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.