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Thread: Simple Question

  1. #1
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    Default Simple Question

    Question:
    A rectangle box without a lid is to be made from 12 square metres of cardboard.
    Find the maximum volume.



    Please try it out before looking at the answer






    Answer 1:
    You can use trial and error.








    Answer 2:
    Let x, y and z be the length width and height of box. We want to maximize V(x,y,z) = xyz subject to the constraint g(x,y,z) = 2xz + 2yz + xy = 12

    Find the answer by using the Method of Lagrange Multiplier








    Final Answer:
    The answer is 4 cube metres.

  2. #2
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    Default

    Is Lagrange Multiplier like optimization?
    Oh Hai Dar

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    yes! but there are cases in which lagrange multipliers fail

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    Default

    4 m(power of 3-cubed)

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    Default

    I assume this would be like the optimization stated above, where you want to optimize the volume.

    V = xyz
    A = 2xy + 2xz + 1yz (minus top)

    And I actually forget how to do the rest from here. God damnit, I had to know this for calc 1...

    dV/dx = yz
    A = 2xy + 2xz + dV/dx

    I forget what to do. Ah well

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