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Math Help - Maximizing and minimizing

  1. #1
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    Maximizing and minimizing

    Hi, I've got 3 problems that I'm really stuck on, but I'll post the first one.
    Any help MUCH appreciated because the assignment is due in about 14 hours.

    1. Maximize P=xyz with x+z=12, y+z=12, and x,y,and z >=0
    The farthest I got on this one was to rearrange the variables to make z the only unknown, then taking the derivative, but I'm stuck from there.

    the last part I have written on it is 16z+z^2 = 48
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by leviathanwave View Post
    Hi, I've got 3 problems that I'm really stuck on, but I'll post the first one.
    Any help MUCH appreciated because the assignment is due in about 14 hours.

    1. Maximize P=xyz with x+z=12, y+z=12, and x,y,and z >=0
    The farthest I got on this one was to rearrange the variables to make z the only unknown, then taking the derivative, but I'm stuck from there.

    the last part I have written on it is 16z+z^2 = 48
    that equation is wrong. after substituting for x and y and differentiating and setting the derivative to zero, you should end up with: z^2 -16z + 48 = 0

    now just find the vertex of that. (for the vertex, z = \frac {-b}{2a}, where a is the coefficient of z^2 and b is the coefficient of z)
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  3. #3
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    oh so I don't have to use the quadratic formula?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by leviathanwave View Post
    oh so I don't have to use the quadratic formula?
    no, we use the quadratic formula to solve for the zeros of a quadratic. you don't want the zeros, you want the vertex
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