Consider the following variant of the knapsack problem. Given are n items with costs ci and volumes vi, and a lower bound on the volume V . Find a minimum cost set of items, such that the total volume is at least V. you should solve it it's the normal knapsack problem, but with an additional lowerbound that the knapsack should be filled AT LEAST

here are some test cases that you can use:

Example: In normal Knapsack, the solution would be Item A, because of the 100 profit.

* However, because of the lowerbound of 85, Item A cannot be chosen.

* The solution here is therefore Item B + Item C */

where item A = (cost: 100, volume:80)

item B = (cost: 40, volume:45)

item C = (cost: 40, volume:45)