CS301 Assignment 5
Suppose that you are given a set T of projects where each project t ∈ T is associated with
• a positive integer et denoting the amount of effort (e.g., the amount of time
or energy) required to complete the project t, and
• a positive integer pt denoting the profit gained by completing the project t.
Given a positive integer c denoting the maximum amount of effort that you can
spend on these projects, the goal is to find the largest amount of profit that you can
make by completing a subset of these projects such that the total amount of effort
spent to complete the projects is at most c.
1. (50 points) State the decision version of this optimization problem: Input?
Output?
2. (50 points) Prove that the decision version is in NP.
A pdf copy of your own solutions (at most one page) should be submitted at
SUCourse+.
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