Question: you are given that . (P) is a maximization LP. (D) is the dual LP of (P). suppose (IP) is the integer program obtained

you are given that . (P) is a maximization LP. (D) is

you are given that . (P) is a maximization LP. (D) is the dual LP of (P). suppose (IP) is the integer program obtained from (P) by adding the constraint "x integer". (ID) is the integer program obtained from (D) by adding the constraint "y integer". For each of the following scenarios, determine if it is possible and does not contradict the above, or that it is impossible. If it's possible, give one example of such a pair of LPs (P) and (D). If it's impossible, briefly explain why. (a) (P) has optimal value 8 and (D) has optimal value 10. (b) Both (IP) and (ID) are infeasible. (c) (ID) has optimal value 8, while (D) has optimal value 10. (d) (IP) is infeasible and (P) is unbounded. (e) (IP) has optimal value 8 and (ID) has optimal value 10.

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