The Unit Knapsack problem is as follows. There is a knapsack of capacity b$0$ litres, and there are n

items, where each item j $=1,...,$ n has a size of aj litres per unit and a profit of cj dollars per unit.

At most one unit of each item may be put into the knapsack. The goal is to fill the knapsack with

one or more items such that the total profit of the items in th