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Phillip, the proprietor of a vineyard, estimates that the first 9600 bottles of wine produced this season will fetch a profit of $5 per bottle. However, the profit from each bottle beyond 9600 drops by $0.0002 for each additional bottle sold. Assuming at least 9600 bottles of wine are produced and sold, what is the maximum profit? (Round your answer correct to the nearest cent.)
$ ?

What would be the profit/bottle in this case? (Round the number of bottles down to the nearest whole bottle. Round your answer correct to the nearest cent.)
$ ?

  • math -

    profit/bottle is 5.00 - 0.0002(x-9600) for x bottles, x > 9600

    total profit is thus

    p(x) = 5*9600 + (x-9600)(5.00 - 0.0002(x-9600))
    = -.0002x^2 + 8.84x - 18432

    This is a parabola opening downward, with vertex at x = 22100

    p(22100) = 79250

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