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practice_prelim1(1)

# practice_prelim1(1) - 1(a[2 marks Dene the term extreme...

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1. (a) [2 marks] Define the term extreme point . Now consider a system of constraints Ax = b x 0 . Suppose that the vector [2 , 3 , 0 , 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

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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 0 x 1 , x 2 , x 3 0 . 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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