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Knapsack Problem

Posted on 2009-04-04
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Last Modified: 2012-06-27
I am uncertain how to solve the following problem and would like some guidance in doing so. Any help is greatly appreciated. Thank you in advance!

Find a subset of the 12 experiments with a total weight of 700 kilograms and a total rating of 49.

Below is a list of the rating and weights, respectively:

9 / 264
8 / 65
8 / 104
8 / 203
7 / 80
6 / 7
6 / 170
6 / 188
5 / 36
4 / 22
3 / 25
2 / 92
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Question by:ssharp77
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blissbear earned 450 total points
ID: 24070100
Well, I would start by realizing the exclusion subset is smaller in total. If you add up all the weights, you will find they total 72, which means you need to exclude items which would total 23 kg.  The total rating for the entire set is 1256, so you need to exclude 556.

Can you determine a subset that meets these totals?
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by:blissbear
blissbear earned 450 total points
ID: 24070106
Also, the total weight is 700 kg, so you can start finding subsets that total to a factor of 10, since those subsets have to add up to be divisible by 10.
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by:blissbear
ID: 24070109
Otherwise, here are your fomulae: http://en.wikipedia.org/wiki/Knapsack_problem :)
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by:GwynforWeb
GwynforWeb earned 50 total points
ID: 24071899
This is not a knapsack problem, although it is similar. The knapsack problem would read,

"Find a subset of the 12 experiments with a total weight of not exceeding 700 kilograms that maximizes the total rating."

I am guessing that a dynamic programming approach could be used for this as well.
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Author Closing Comment

by:ssharp77
ID: 31566695
Thank you.
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by:GwynforWeb
ID: 24073096
I would have been interested to know if this problem is to be solved as exactly stated or is in fact just a knapsack problem.   As stated the problem can also be formulated as a dynamic programming problem.
(note: the link refers to the knapsack not this problem although it is a guide to the solution formulation)
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