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pafoo

  • 3 years ago

A company has determined that when x items are sold daily, the profit P is given by P(x)=-0.002x^2+4.3x-120 What is the profit if 700 items are made? How many items should be made daily in order to maximize the companys profit? I know the first one is 1,910, but how do I maximize the company's profit?

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  1. RyanL.
    • 3 years ago
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    This basically asks you to find the vertex of the equation

  2. RyanL.
    • 3 years ago
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    find the derivative and set it to zero

  3. RyanL.
    • 3 years ago
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    solve for x then

  4. pafoo
    • 3 years ago
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    What formula would I use?

  5. RyanL.
    • 3 years ago
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    I don't know any formulas but I do know how to find it using a derivative

  6. pafoo
    • 3 years ago
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    Ok, any advice on how I should proceed?

  7. RyanL.
    • 3 years ago
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    Find the derivative

  8. pafoo
    • 3 years ago
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    So if I get a derivative of 4.3-0.004x, what should I do then?

  9. RyanL.
    • 3 years ago
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    set it to zero and solve for x

  10. RyanL.
    • 3 years ago
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    4.3-0.004x=0

  11. RyanL.
    • 3 years ago
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    4.3-0.004x=0 -0.004x=-4.3 x=-4.3/-0.004 x=1075

  12. RyanL.
    • 3 years ago
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    1075 items

  13. pafoo
    • 3 years ago
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    i see, so the derivative is the key, awesome, thanks!

  14. RyanL.
    • 3 years ago
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    http://www.wolframalpha.com/input/?i=-0.002x%5E2%2B4.3x-120 if you graph it you can see the highest point right? That point is called the vertex and you can find it using the derivative

  15. pafoo
    • 3 years ago
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    Ah, ok I got you.

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