SOLUTION: a carpenter can construct bookcases at a cost of 40 each. if the carpenter sells the bookcases for x dollars each, it is estimated that 300-2x bookcases will be sold per month. det

Question 911382: a carpenter can construct bookcases at a cost of 40 each. if the carpenter sells the bookcases for x dollars each, it is estimated that 300-2x bookcases will be sold per month. determine the selling price of each bookcase that will give the carpenter the greatest monthly profit.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
a carpenter can construct bookcases at a cost of 40 each. if the carpenter sells the bookcases for x dollars each, it is estimated that 300-2x bookcases will be sold per month. determine the selling price of each bookcase that will give the carpenter the greatest monthly profit.
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Cost to produce 300-2x bookcases = 40(300-2x) = 12000-80x dollars
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Revenus when 300-2x bookcases are sold : (300-2x)x = 300x - 2x^2
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Profit = (revenue-cost) = -2x^2 + 380x - 12000
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Maximum profit occurs when x = -b/(2a) = -380/(2*-2) = 95
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Cheers,
Stan H.
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