Q:

Find combination that gives maximum profit

Say I have table that looks like this:
ID | Cost | Profit
1 | 0.55 | 1.24
2 | 0.23 | 3.11
3 | 0.19 | 2.21
4 | 0.53 | 1.49
... and so on. 
How do I find the maximum profit if my budget is of certain value?  ie: Find max profit with cost of 1.12.  If from the table above, I should take item from ID 2  + 3 + 4 to maximize my profit. 
I'm trying to google something from LP, Operation Research but I'm really Googling blindly, I don't know what are the keywords I should look for.  Please help.  

A:

What you need is 0/1 Knapsack!  I have assumed from the example you gave that you need to take the item as a whole and not a fraction of the item.  Otherwise go for default (Fractional) Knapsack. 
Get to know about the greedy version of solution & why it might fail, then the Fractional Knapsack Dynamic Programming style of solution for this problem and then 0/1 Knapsack!  This is how you should learn to solve this problem. 
Let me know if you need anything else on this.