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Math Help - optimization - maximizing profit

  1. #1
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    optimization - maximizing profit

    the sale price of an item is 800-35x dollars and the total manufacturing cost is 2x^3-140x^2+2,600x+10,000 dollars, where x is the number of items. What number of items should be manufactured in order to optimize the manufacturer's total profit?
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    Quote Originally Posted by yoman360 View Post
    the sale price of an item is 800-35x dollars and the total manufacturing cost is 2x^3-140x^2+2,600x+10,000 dollars, where x is the number of items. What number of items should be manufactured in order to optimize the manufacturer's total profit?
    Profit = Revenue - Cost =  (800-35x)-(2x^3 - 140x^2 + 2600x + 10000)

    Just differentiate and find the max.
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  3. #3
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    Quote Originally Posted by Gusbob View Post
    Profit = Revenue - Cost =  (800-35x)-(2x^3 - 140x^2 + 2600x + 10000)

    Just differentiate and find the max.
    I tried that and but it does not have a max. i even graphed it on calculator and the derivative does not cross x-axis
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  4. #4
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    Quote Originally Posted by yoman360 View Post
    I tried that and but it does not have a max. i even graphed it on calculator and the derivative does not cross x-axis
    Try again and make sure the signs are correct.

    Wolfram|Alpha
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  5. #5
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    Quote Originally Posted by Gusbob View Post
    Try again and make sure the signs are correct.

    Wolfram|Alpha
    Thanks. i just made a stupid mistake
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