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Math Help - Optimization problem. Can u help?

  1. #1
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    Optimization problem. Can u help?

    Can anyone help? Here's the problem:

    Optimization Problem.

    Here's the question:
    A box with open top is to be constracted from a square piece of cardboard 3feet wide,by cutting out a square from each of the corners and bending up the sides. Find the largest volume that sucha box can have.
    a) Picture: Draw a diagram illustrating the general situation.
    b) Objective: Write an expression representing the volume fo the resulting box.
    c) Help: Make sure that the objective is entirely in terms of one variable, x.
    d) Maximize or Minimize: Find the critical points of the object.
    e) Prove it: Use the closed interval domain check, the 1st derivative or the 2nd derivative test. ( pos says min, neg says max)
    f) Answer the question: Use the variable solution to answer the particular problem's question.
    Last edited by CrxtoZ; October 23rd 2008 at 11:10 AM. Reason: missing info
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  2. #2
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    cut four squares of size x by x from each corner, then fold up the flaps.

    resulting 3D box dimensions are (3-2x) by (3-2x) by x

    V = x(3-2x)^2

    that's the difficult part ... do the calculus and find the value of x that will maximize the volume.

    remember your usable domain ... 0 < x < 3
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