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Problem: given a set of n tasks with execution time Ti, due date Di, and a profit Vi (given only if is enden before due date), is there a task schedule that returns a total profit greater or equal than k knowing that tasks must be executed one at a time?

I am asked to proof that this problem is NP-Complete, can anyone help?

Thanks.

Tomas Botalla
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    Welcome to CS.SE! What did you try? Where did you get stuck? We're happy to help you understand the concepts but just solving exercises for you is unlikely to achieve that. You might want to start by looking at our reference materials: http://meta.cs.stackexchange.com/q/599/755, particularly http://cs.stackexchange.com/q/11209/755 and http://cs.stackexchange.com/q/1240/755. I suggest you work through that material, try to solve your problem again and edit to include your attempts along with the specific problems you encountered. See also http://meta.cs.stackexchange.com/q/1284/755. – D.W. Dec 11 '16 at 02:38

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Since this problem is very approachable, you could first try to think about a greedy solution to show this is in the class P, and thus probably not in NP-complete. Once you have done this you could think about a polytime reduction to a problem known to be in NP-complete. Consult Karp's original 21 problems to get a feel for the type of problems you can use to find this reduction. Once you have done this come back with more specific questions :)

Logan Leland
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