# maximise weights of sticks that can fit in a tube so that sum of lenghts is less than L

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Malloju Dinesh on 28 Feb 2022
Commented: Voss on 2 Mar 2022
1) We define a knaptube problem as follows: Given n sticks of length l1, l2, …, ln, weight w1, w2, …, wn, and a tube of total length L, find a subset of these sticks that can be lined up to fill the tube of length L while maximizing the total weight.
More formally, the objective and the constraint of the knaptube problem are follows, where si ranges over the indices of the selected sticks:
• Objective: Maximize the sum of the weights of the sticks in the tube
max (∑𝑤𝑠𝑖 ) (w subscript si) subject to
• Constraint: The sum of the lengths of the sticks in the tube must be less than or equal to L.
∑ 𝑙𝑠𝑖(l subscript si) ≤ 𝐿.
i am looking for ideas on how to approach this problem . Initially i thought its a simple problem but the more i think about this its looks a tough one .. please let me know on how to approach this .. any ideas are appreciated ..thanks
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Voss on 2 Mar 2022