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This may be a simple question for those know-how guys. But I cannot figure it out by myself.
Suppose there are a large number of objects that I need to select some from. Each object has two known variables: cost and benefit. I have a budget, say $1000. How could I find out which objects I should buy to maximize the total benefit within the given budget? I want a numeric optimization solution. Thanks!
Your problem is called the “knapsack problem”. You can read more on the wikipedia page. Translating the nomenclature from your original question into that of the wikipedia article, your problem’s “cost” is the knapsack problem’s “weight”. Your problem’s “benefit” is the knapsack problem’s “value”.
Finding an exact solution is an NP-complete problem, so be prepared for slow results if you have a lot of objects to choose from!