   Chapter 3.7, Problem 62E

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Textbook Problem

# 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) 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? To determine (a) To find: The demand function assuming that it is linear Explanation 1) Concept: To find the demand function ‘P(x)’ use slope-point formula, y-y1=m(x-x1) slope=m=y2-y1x2-x1 2) Given: P20=10 P18=11 3) Calculation: It is given that the demand function is linear. So, by using slope-point formula construct the demand function. First find the slope, From given information P20=10and P18=11 Therefore, by using formula m=y2-y1x2-x1=10-1120-18 Simplify, m=-12 Therefore, m=-12 Therefore, by using slope-point formula To determine (b) To find: The selling price to maximize the profit if the material for each necklace costs$6

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