Consider a modification to the activity selection problem in which each activity a i has, in addition to a start and finish time, a value i The objective is no longer to maximize the number of activities scheduled, but instead to maximize the total value of the activities scheduled That is, we wish...

We can no longer use the greedy algorithm to solve this problem However as we show the problem still has an optimal substructure which allows us to formulate a dynamic programming solution The analysi ...

Consider a modification to the activity-selection problem in which each activity a i has, in addition to

Question:

Consider a modification to the activity-selection problem in which each activity a_i has, in addition to a start and finish time, a value ν_i. The objective is no longer to maximize the number of activities scheduled, but instead to maximize the total value of the activities scheduled. That is, we wish to choose a set A of compatible activities such that ∑_aki_∈Aν_kis maximized. Give a polynomial-time algorithm for this problem.

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