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May 15th, 2013, 12:17 AM   #1
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Mr Chip and his Chip Boxes

Mr Chip sells chip boxes. His chip boxes are square based rectangular prisms with an open square top. The dimensions of the boxes are 5cm x 5cm x 20cm.

The cardboard used to make the boxes comes in 1m x 1m sheets, and costs 30c per square metre. Mr Chipís customers want the chip boxes to be in the shape of a square based rectangular prism, but do not care what their exact dimensions are. Can Mr Chip save money by changing the dimensions of the chip box? What dimensions would be the most economical?

Explain and mathematically justify your answer. Full mathematical reasoning should be included.
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May 15th, 2013, 05:43 AM   #2
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Re: Mr Chip and his Chip Boxes

Please show all work you have done so far in your attempt to find a solution.

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May 15th, 2013, 07:29 AM   #3
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Check whether 10cm ◊ 10cm ◊ 5cm would be better, for example.
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May 15th, 2013, 10:00 AM   #4
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Re: Mr Chip and his Chip Boxes

Guess we're to assume boxes must have volume of 500 cubic cm.

Cheapest would be the case with minimum surface area.

x = square sides, h = box height.
So you need to minimize x^2 + 4xh where h = 500/x^2.
Let's see your stuff!
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