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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.

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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 :)

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