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Constrained minimization problem

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I just posted this problem in the wrong forum (Computer Help). I think this is the better forum for this question. Sorry for the duplication...

 

In the following problem, which algorithm should be considered?

Having a finite set of variable height brikcs, how can I find the subset that can reach at least a given height, minimizing the total height of the chosen bricks?

In other words, which bricks should I use to reach a given height minimizing cost of material?

 

Thanks.

 
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bin packing algorithms maximize the number of items given the constraint in the sum of volumes.

In may case you have to minimize the sum of volumes, constrained it is more than a given value.

It's not so different, but I cannot get how to pass from one problem to the other

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