he can sell more necklaces, and if he raises the price than he sells fewer neckl

Question

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 Number of necklaces sold 31 24 14 16 (a) Find a linear function of the form n = co + clp that best fits these data, using least squares. n=n(p) = (b) Find the revenue (number of items sold times the price of each item) as a function of price 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) = d) Finally, find the price that will maximize the profit.

Explanation / Answer

So, we get :
n = 47.643 - 2.112p ---> ANS

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Revenue is :
n * p

R = p(47.643 - 2.112p)

R = 47.643p - 2.112p^2 ---> ANS

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Profit :
Revenue - cost

Now, for p necklaces, he spends 5*p = 5p dollars for material cost

So,
P(p) = 47.643p - 2.112p^2 - (5p)

P(p) = 42.643p - 2.112p^2 ---> ANS

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d)
For max profit,
dP/dp = 0

42.643 - 4.224p = 0

p = 10.09 dollars approx

If this doesnt work
try 10.10 dollars

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