Consider a variation on the previous problem. In the new scenario, any application can potentially be moved, but now some of the benefits bi for moving to the new system are in fact negative:lf bi<0, then it is preferable (by an amount quantified in bi) to keep i on the old system. Again, give a polynomial-time algorithm to find a set S ⊆ {1,2, … n} for which the sum of the benefits minus the expenses of moving the applications in S to the new system is maximized.
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