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Math Help - Quadratic equation optimization with volume

  1. #1
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    Quadratic equation optimization with volume

    "Economite Plastics plans to produce a one-compartment vertical file by bending the long side of an 8-in by 14-in. sheet of plastic along two lines to form a U shape. How tall should the file be in order to maximize the volume that the file can hold?"

    Can you guys help me determine what the constraints are for this particular problem with an explanation of why that is so? After I find that out, I can solve it.... thanks.
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  2. #2
    MHF Contributor Unknown008's Avatar
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    If I understand the prolem well, you can fold the sheet in two ways, but only one will give the maximum volume.

    Code:
    ____________
    |          |   x
    |__________|
    |          |   y
    |__________|      8
    |          |   x
    |__________|
    
         14
    or

    Code:
    ____________
    |   |   |   |
    |   |   |   | 8
    |   |   |   |
    |___|___|___|
      x   y   x
    
         14
    To maximise volume in each case, the height is x and the width y.

    In the first case, 2x + y = 8
    V = 14xy

    In the second case, 2x + y = 14
    V = 8xy

    Look for the one with maximum volume!
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