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Unformatted text preview: x 2 without bound which means that the objective can increase without bound as well. 3.3.5 (2 points) True. Consider the contrapositive of the statement, namely if the LPs feasible region is bounded, then the LPs objective is also bounded. Clearly this statement is true, for if the feasible region is bounded, then every feasible solution (which includes the optimal solution) has nite values for all variables. Any linear function of nite values is also nite, so the LPs objective is bounded. 3.3.6 (2 points) False. A counterexample to this statement is the following very simple LP: min x 1 + x 2 s.t. x 1 , x 2 This LPs feasible region is unbounded since x 1 and x 2 can take any non-negative value. However the optimal solution is clearly x 1 = 0 , x 2 = 0. 2...
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- Spring '07