Question: In class we talked about linear programming, and the fact that it can be solved in polynomial time. Slightly more formally, we defined the feasibility

In class we talked about linear programming, and the fact that it can be solved in polynomial time. Slightly more formally, we defined the feasibility version of linear programming to be the following decision problem Input: n variables x1, x2, . . . , xn, and m linear inequalities over the variables. Output: YES if there is a way of assigning each variable a value in R so that all m linear constraints are satisfied, NO otherwise. Let Integer Linear Programming be the same problem, but where each variable is only allowed to take values in Z rather than in R. (a) (15 points) Prove that Integer Linear Programming is in NP. (b) (35 points) Prove that Integer Linear Programming is NP-hard

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