Challenge: Maximum Value of the Loot

Problem

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Maximizing the Value of the Loot Problem

Find the maximal value of items that fit into the backpack.

Input: The capacity of a backpack $W$, as well as the weights $(w_{1} ,\ldots,w_{n})$ and costs $(c_{1},\ldots, c_{n})$ of $n$ different compounds.

Output: The maximum total value of fractions of items that fit into the backpack of the given capacity, i.e., the maximum value of $c_{1}·f_{1}+\ldots+c_{n}·f_{n}$ such that $w_1\cdot f_1+\dots +w_{}$ ...