moterpoker

Nevermind. I found the answer. It is 0-1 Knapsack problem

Hi all, I need a little help regarding simple optimization: There are a given number of pairs of positive numbers for e.g. [latex](a_1, b_1), (a_2, b_2)... (a_N, b_N)[/latex]. The objective is to choose a subset [latex]S[/latex] of some pairs: [latex]\max \sum_{i \in S} a_i[/latex] s.t [latex]\sum_{i \in S} b_i\le B[/latex] In other words, this problem can be thought as follows: You have some bank balance [latex]B[/latex] and there are number of different products in the market of price lets say [latex]b_i[/latex] that give some utility [latex]a_i[/latex]. Objective is to maximi