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Help with Optimization Problem

  1. Oct 11, 2005 #1
    If an open box has a square base and volume of 108 in.3 and is constructed from a tin sheet, find the dimensions of the box, assuming a minimum amount of material is used in its construction.

    :confused: don't even know where to start on this problem.
  2. jcsd
  3. Oct 11, 2005 #2
    Find expressions describing the volume and surface area of the box, you want to maximize volume and minimized surface area.
  4. Oct 12, 2005 #3


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    Homework Helper

    The key is to write what you are given in mathematical terms. For example, you can use V to indicate volume, A to indicate area, x and y to indicate the dimensions of the base and z to indicate the height.

    1. Write an equation for V in terms of x, y, z. Hint: what do you know about x & y?

    2. Write an equation for A in terms of x, y, z. Hint: the box is open

    3. Combining 1 & 2 should give you an expression for A in terms of a single variable

    4. You want to minimize A. Hint: in calculus what do you do w/ min/max problems?
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