Suppose I need exactly $X$ flowerpots.

I have $Y$ flowerpots to choose from, and $Y > X$.

Each of the $Y$ flowerpots has a cost and a capacity. I have a fixed budget to buy flowerpots. The budget, and costs and capacity of each flowerpot are all strictly positive integers. Assume that the total cost of the cheapest $X$ flowerpots do not exceed my budget.

My goal is to maximize total capacity subject to not exceeding my budget (I can spend less, but not more).

If I didn't need exactly $X$ flowerpots, this is the standard 0/1 knapsack problem. However, I need exactly $X$ flowerpots.

What does this problem become, and what algorithm can I use to solve this?

  • $\begingroup$ What did you try, where did you get stuck? It is not hard to modify the dynamic programming approach to the Knapsack to solve this problem, for example. $\endgroup$ Jul 9 '19 at 4:01
  • $\begingroup$ Have you seen this question? cs.stackexchange.com/questions/18492/… $\endgroup$
    – phan801
    Jul 9 '19 at 12:11

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