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Unformatted text preview: 1. (a) [2 marks] Define the term extreme point . Now consider a system of constraints Ax = b x . Suppose that the vector [2 , 3 , , 4 , 0] T is a basic feasible solution, and that the vector [0 , 1 , 2 , 2 , 4] T is a feasible solution that may or may not be basic. Answer the following questions, justifying your answers carefully . (b) [2 marks] Exactly one of the following statements is correct. State which one, and explain why it is correct. (i) A must have no more than 3 rows. (ii) A must have at least 3 rows. (c) [2 marks] Find an extreme point of the feasible region. (d) [2 marks] Find a feasible solution that is not an extreme point of the feasible region. 1 2. [6 marks] Use the simplex method to solve the linear program maximize x 1 x 2 x 3 subject to 2 x 1 + x 2 x 3 2 3 x 1 + 2 x 2 4 x 1 + x 3 x 1 , x 2 , x 3 . At each iteration, list the basic variables, the corresponding basic feasible solution, its objective value, and the entering and leaving variables....
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This note was uploaded on 10/31/2011 for the course OR&IE 3300 at Cornell University (Engineering School).
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