TITLE: Curious minimization problem
QUESTION [0 upvotes]: Well, this problem may look easy, but I'm not able to get the equations to minimize.
We have a hole in the floor and need to make a lid for it so that:
i) It can never fall into the hole, that is, the lid cannot pass through the constructed hole, in no position. We understand that the cap is slightly larger than the hole
(with the same shape) and that at the bottom of the lid there is a small edge, very close to the edge of the lid, to fit the gap.
ii) We have some flat rectangular metal plates, a little less than 70 centimeters inwide by three meters long. These plates must be able to pass through the hole.
iii) They should use the least amount of material possible, to minimize costs, but respecting
the above requirements.
We are asked to get the exact area of the lid.
Any help to translate it to a math language and how to solve it, would be really nice.

REPLY [0 votes]: Make the hole just large enough to pass the plate through, something like 1 cm by 70 cm.  The problem is that you can orient the lid with the 70 cm longways.  You need a thick part of the lid that is more than 1 cm.  It doesn't need to be much.  A 1.25 by 1.25 cm part on the end of the lid will be enough.  There is no absolute minimum for the lid, as it needs to be wider than 1 cm but can be any amount wider.
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