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May 15th, 2013, 12:17 AM  #1 
Newbie Joined: May 2013 Posts: 1 Thanks: 0  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 Chip’s 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. 
May 15th, 2013, 05:43 AM  #2 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: Mr Chip and his Chip Boxes
Please show all work you have done so far in your attempt to find a solution. 
May 15th, 2013, 07:29 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,384 Thanks: 2011 
Check whether 10cm × 10cm × 5cm would be better, for example.

May 15th, 2013, 10:00 AM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,145 Thanks: 1003  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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