A community bird-watching society makes and sells simple bird feeders to raise money for its conservation activities. The materials for each feeder cost $4, and the society sells an average of 28 perweek at a price of $8 each. The society has been considering raising the price, so it conducts a survey and finds that for every dollar increase, it loses 2 sales per week.(a) Find a function that models weekly profit in terms of price per feeder. (Let x represent the price per feeder and P represent the profit.)P(x)(b) What price should the society charge for each feeder to maximize profits?$What is the maximum weekly profit?

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Asked Oct 6, 2019
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A community bird-watching society makes and sells simple bird feeders to raise money for its conservation activities. The materials for each feeder cost $4, and the society sells an average of 28 per
week at a price of $8 each. The society has been considering raising the price, so it conducts a survey and finds that for every dollar increase, it loses 2 sales per week.
(a) Find a function that models weekly profit in terms of price per feeder. (Let x represent the price per feeder and P represent the profit.)
P(x)
(b) What price should the society charge for each feeder to maximize profits?
$
What is the maximum weekly profit?
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A community bird-watching society makes and sells simple bird feeders to raise money for its conservation activities. The materials for each feeder cost $4, and the society sells an average of 28 per week at a price of $8 each. The society has been considering raising the price, so it conducts a survey and finds that for every dollar increase, it loses 2 sales per week. (a) Find a function that models weekly profit in terms of price per feeder. (Let x represent the price per feeder and P represent the profit.) P(x) (b) What price should the society charge for each feeder to maximize profits? $ What is the maximum weekly profit?

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Expert Answer

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(a) Let x be the price per feeder which is the selling price and p be the pro...

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28 2(x-8) 28 - 2x +16 -2x44 Therefore, the cost of feeder sold is, 4-2r44-8.x +176 Revenue is, x-2x+ 44) Therefore, the profit is = Revenue - Cost (-2x +44)x-4)= -2x2+52x -176 That is, P(x)2r2 +52.r-176

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