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| Math Central | Quandaries & Queries |
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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. |
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
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