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

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

[Voss]

These links may be useful:

https://en.wikipedia.org/wiki/Knapsack_problem

https://en.wikipedia.org/wiki/List_of_knapsack_problems