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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 LP’s feasible region is bounded, then the LP’s 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 ﬁnite values for all variables. Any linear function of ﬁnite values is also ﬁnite, so the LP’s 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 LP’s 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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This note was uploaded on 04/02/2008 for the course IEOR 162 taught by Professor Zhang during the Spring '07 term at Berkeley.
- Spring '07