L27 - CO350 Linear Programming Chapter 9 The Revised...

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Unformatted text preview: CO350 Linear Programming Chapter 9: The Revised Simplex Method 8th July 2005 Chapter 9: Revised Simplex Method 1 Example of unboundedness Solve the LP using revised simplex method with smallest- subscript rules. ( P ) max 3 x 1- 2 x 2- 3 x 3 s.t. x 1- x 2- x 3 ≤ 1 7 x 1- 8 x 2- 11 x 3 ≤ 2 2 x 1- 2 x 2- 3 x 3 ≤ 1 x 1 , x 2 , x 3 ≥ Adding slack variables x 4 , x 5 , x 6 gives ( P ) max c T x s.t. Ax = b x ≥ where A = 2 6 6 6 4 1- 1- 1 1 0 0 7- 8- 11 0 1 0 2- 2- 3 0 0 1 3 7 7 7 5 , b = 2 6 6 6 4 1 2 1 3 7 7 7 5 and c = [3 ,- 2 ,- 3 , , , 0] T Start from feasible basis B = { 4 , 5 , 6 } . Chapter 9: Revised Simplex Method 2 Iteration 1: B = { 4 , 5 , 6 } , x * B = 2 6 6 6 4 1 2 1 3 7 7 7 5 , A B = 2 6 6 6 4 1 0 0 0 1 0 0 0 1 3 7 7 7 5 . Solve A T B y = c B = 2 6 6 6 4 3 7 7 7 5 to get y = 2 6 6 6 4 3 7 7 7 5 . Compute ¯ c 1 = c 1- A T 1 y = 3- [ 1 7 2 ] y = 3 > . x 1 enters. Solve A B d = A 1 to get d = 2 6 6 6 4 1 7 2 3 7 7 7 5 . t = min { 1 1 , 2 7 , 1 2 } = 2 7 . x 5 leaves. Update x * 1 = t = 2 7 , x * 4 = 1- (1)( 2 7 ) = 5 7 , x * 6 = 1- (2)( 2 7 ) = 3 7 ....
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This note was uploaded on 06/11/2011 for the course C 350 taught by Professor Wolkowicz during the Fall '97 term at Waterloo.

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L27 - CO350 Linear Programming Chapter 9 The Revised...

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