# Homework Help: Optimisation question

1. Aug 29, 2004

### chemical

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

The teacher also said something about the Golden Ratio, but i cant see any relation to this in the dimensions

2. Aug 31, 2004

### robphy

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/ )

3. Aug 31, 2004

### Locrian

I'm going to go with door #2 robphy.

4. Aug 31, 2004

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.

5. Aug 31, 2004

### Tom McCurdy

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.

6. Sep 1, 2004

### HallsofIvy

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?

7. Sep 1, 2004

the golgen ratio IS 1:1:1. The only reason the companies dont make it this is because of appeal, advertisement and other factors.

8. Sep 5, 2004

### chemical

1:1:1 is the optimal ratio, not the golden ratio. Thanks for the comments guys :)

9. Sep 5, 2004

### HallsofIvy

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