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Math Help - profit maximization unconstrainted

  1. #1
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    profit maximization unconstrainted

    I have the eq. f(x,y) = 2x^2 + x^2y + y^3 + 12y^2
    trying to find the stationary points for this eq.
    i have the p.derivatives at:
    fx = 4x - 2xy
    fy = x^2 + 3y^2 + 24y
    fxx = 4 + 2y
    fyy = 6y + 25
    fxy = 2x

    my issue lies is that i need to find the 4 stationary points

    for fx i have factored out to reach fx=x(4 + 2y)
    and for fy = x^2 + y(3y + 24)

    from here i am unsure how i get my x and y points if someone could show me how to go from here it would be very helpful
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  2. #2
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    Quote Originally Posted by manichee View Post
    I have the eq. f(x,y) = 2x^2 + x^2y + y^3 + 12y^2
    trying to find the stationary points for this eq.
    i have the p.derivatives at:
    fx = 4x - 2xy
    fy = x^2 + 3y^2 + 24y
    fxx = 4 + 2y
    fyy = 6y + 25
    fxy = 2x

    my issue lies is that i need to find the 4 stationary points

    for fx i have factored out to reach fx=x(4 + 2y)
    and for fy = x^2 + y(3y + 24)

    from here i am unsure how i get my x and y points if someone could show me how to go from here it would be very helpful

    you have a typo: it's + instead - in f_x.

    Now, we have x(4+2y)=0 \Longleftrightarrow x=0\,\,or\,\,y=-2. Plug in these values in f_y and find the possible values for y in each case.

    Tonio
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  3. #3
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    so i do thanks for picking that up wats the maths behind just saying x = 0 and y = -2? i know thats what i have to do but im not sure in the actual steps involved in getting there
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