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Mathematics - Calculus - Maximizing Profit

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Profit -

A manufacturer has been selling lamps at $6 apiece, and at this price, consumers have been buying 3,000 lamps per month. The manufacturer wishes to raise the price and estimates that for each $1 increase in price, 1,000 fewer lamps will be sold each month. The manufacturer can produce the lamps at a cost of $4 per lamp. At what price should the manufacturer sell the lamps to generate the greatest possible profit?

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Let the manufacturer make x units of one dollar increase in price. Then his new revenue will

be R(x) = cost x quantity = (6 + ...

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