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Thread: Word Problem#2

  1. #1
    May 2006

    Word Problem#2

    A small company produces and sells x widgets per week. Their cost function in dollars in C(x)=50+3x and their revenue function in dollars is R(x)=(6x-x²)

    How many widgets per week should be produced for maximum profit?

    (FYI. A widget is "a gadget" or "an unnamed or hypothetical manufactured article">)
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  2. #2
    MHF Contributor
    Oct 2005
    I see you've posted a bunch of problems. I personally don't like to answer problems in bulk like this when I don't see you've tried to answer them. For the other posts, maybe you could show some work to help us out.

    So the profit (assuming we make more money than we lose) is revenue - cost.

    So we have $\displaystyle [R(x) \times x] - [(C(x) \times x]$

    Using the given functions this comes out to [tex](6x^2-x^3)-(50+3x^2)]/math]. Now differentiate and set it equal to zero to find a max.
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