Maximizing total value given bound on total cost I have a list of pairs with values and costs:

    | value | cost |       
    11, 1000    
    7, 700
    7, 700
    6, 700
    2, 400
    2, 500
    1, 600


The list is ordered by value/cost decreasingly.
The task is, given a budget X find the maximum value you can get while keeping the total cost within the budget.
In the sample example, if X=1400, the maximum value would be 14.

What algorithm would be the most efficient to find this value?
Your problem is KNAPSACK, one of the classic NP-complete problems. Wikipedia contains a wealth of information about the problem, include exact and approximation algorithms.