True or False. No justification required. If an integer linear program [P] has a

Question

True or False. No justification required. If an integer linear program [P] has a feasible solution, then its LP relaxation must also have a feasible solution. If the LP relaxation of an integer LP [P] is infeasible, then the integer LP [P] is also infeasible. The optimal value of the objective function of an integer LP (in minimization form) is always smaller than the optimal value of the objective function of its LP relaxation. Rounding an optimal solution to the LP relaxation of an integer linear program [P] always yields a feasible solution to [P]. solution of an LP relaxation is always a solution of the associated integer LP. If a solution of an LP relaxation is integer, then it must be an optimal solution of the associated integer LP.

Explanation / Answer

Solution:

(a): False

if an integer linear program has feasible solution then its LP may have infeasible solution

(b): False

if an integer linear program has infeasible solution then its LP may have feasible solution

(c):True

(d):False

(e)True

(f):True

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