During the summer months Terry makes and sells necklaces on the beach. Terry notices that if he lowers the price, he can sell more necklaces, and if he raises the price than he sells feve necklaces. The table below shows how the number n of necklaces sold in one day depends on the price p in dollars). Price 7 12 16 Number of necklaces sold 35 25 11 a) Find a linear function of the form rco + cp that best fits these data, using least squares. b) Find the revenue (number of items sold times the price of each item) as a function of price p R-R(p) e) If the material for each necklace costs Terry 5 dollars, find the profit (revenue minus cost of the material) as a function of price p. P-P(p) - d) Finally, find the price that will maximize the profit.
During the summer months Terry makes and sells necklaces on the beach. Terry notices that if he lowers the price, he can sell more necklaces, and if he raises the price than he sells feve necklaces. The table below shows how the number n of necklaces sold in one day depends on the price p in dollars). Price 7 12 16 Number of necklaces sold 35 25 11 a) Find a linear function of the form rco + cp that best fits these data, using least squares. b) Find the revenue (number of items sold times the price of each item) as a function of price p R-R(p) e) If the material for each necklace costs Terry 5 dollars, find the profit (revenue minus cost of the material) as a function of price p. P-P(p) - d) Finally, find the price that will maximize the profit.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:During the summer months Terry makes and sells necklaces on the beach. Terry notices that if he lowers the price, he can sell more necklaces, and if he raises the price than he sells fewer
necklaces. The table below shows how the number n of necklaces sold in one day depends on the price p in dollars).
Price
7
12
16
Number of necklaces sold
35
25
11
(a) Find a linear function of the form n=co+cip that best fits these data, using least squares.
n = n(p) =
(d) Finally, find the price that will maximize the profit.
P
(b) Find the revenue (number of items sold times the price of each item) as a function of price p
R = R(p) =
(c) If the material for each necklace costs Terry 5 dollars, find the profit (revenue minus cost of the material) as a function of price p.
P= P(p) =
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