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Homework Help: Optimisation question

  1. Aug 29, 2004 #1
    I have been given a problem of taking an object (I used a Cornflakes Box) and finding the optimal surface area compared to its volume (volume and ratio between sides constant)

    I got:

    Cornflakes Box :
    Length = 25cm
    Height = 36 cm
    Width = 9 cm

    Optimal Surface area box:
    Length = 17.3 cm
    Height = 43.28 cm
    Width = 10.82

    Overall a 90cm^2 difference in surface area.

    Now I have to explain why Cornflakes would make a box with a greater surface area, thus costing more. Please help :confused:


    The teacher also said something about the Golden Ratio, but i cant see any relation to this in the dimensions
     
  2. jcsd
  3. Aug 31, 2004 #2

    robphy

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    Some ideas. (I don't know the real answer.)

    Is the Corn Flakes box
    • just right for the average [child's] hand to hold?
    • more stable against tipping over?
    • better for packing/tiling?
      (Interesting: http://www.scamecanica.com/qpm/examples/ )
    • better for occupying more advertising space on your grocer's shelf?
     
  4. Aug 31, 2004 #3
    I'm going to go with door #2 robphy.
     
  5. Aug 31, 2004 #4
    Ill give you the golden ratio: 1:1:1 (a CUbe)

    Waht dont you get about which one would cost more. The box with the larger surface ares costs more. Its that simple.
     
  6. Aug 31, 2004 #5
    But who wants to pour cereal out of a cube-- plus its built into the mind of the consumer that that is the shape. It has all to deal with appeal to the consumer.
     
  7. Sep 1, 2004 #6

    HallsofIvy

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    No, that is not the golden ratio. And if you had read the original post, the question was WHY would the cereal makers use a box that cost more. You appear to be saying that cereal makers use a box with more area BECAUSE it costs more. Do you really think they enjoy paying more money?
     
  8. Sep 1, 2004 #7
    the golgen ratio IS 1:1:1. The only reason the companies dont make it this is because of appeal, advertisement and other factors.
     
  9. Sep 5, 2004 #8
    1:1:1 is the optimal ratio, not the golden ratio. Thanks for the comments guys :)
     
  10. Sep 5, 2004 #9

    HallsofIvy

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    It may be the "golgen" ratio but it certainly isn't the "golden ratio".
     
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