hw08solutions - IEOR 162 Linear Programming Spring 2007...

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Unformatted text preview: IEOR 162 Linear Programming Spring 2007 Homework 8 Solutions 4.12.1 (4 points) Standard Form with artificial variables: max- 4 x 1- 4 x 2- x 3- Ma 3 s.t. x 1 + x 2 + x 3 + s 1 = 2 2 x 1 + x 2 + s 2 = 3 2 x 1 + x 2 + 3 x 3- e 3 + a 3 = 3 x 1 , x 2 , x 3 , s 1 , s 2 , e 3 , a 3 ≥ Solve using big-M method: ↓ z x 1 x 2 x 3 s 1 s 2 e 3 a 3 RHS ratio 1 4- 2 M 4- M 1- 3 M M- 3 M 1 1 1 1 2 2 2 1 1 3- 2 1 3- 1 1 3 1 z x 1 x 2 x 3 s 1 s 2 e 3 a 3 RHS 1 10 3 11 3 1 3- 1 3 + M- 1 1 3 2 3 1 1 3- 1 3 1 2 1 1 3 2 3 1 3 1- 1 3 1 3 1 The final tableau represents an optimal solution ( x 1 , x 2 , x 3 ) = (0 , , 1) , z = 1. Remember that the original objective was minimization which is why z = 1. 4.12.5 (4 points) Standard form with artificial variables: max- x 1- x 2- Ma 1- Ma 2 s.t. 2 x 1 + x 2 + x 3 + a 1 = 4 x 1 + x 2 + 2 x 3 + a 2 = 2 x 1 , x 2 , x 3 , a 1 , a 2 ≥ Solve using big-M method: ↓ z x 1 x 2 x 3 a 1 a 2 RHS ratio 1 1- 3 M 1- 2 M- 3 M- 6 M 2 1 1 1 4 2 1 1 2 1 2 2 z x 1 x 2 x 3 a 1 a...
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This homework help was uploaded on 04/02/2008 for the course IEOR 162 taught by Professor Zhang during the Spring '07 term at University of California, Berkeley.

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hw08solutions - IEOR 162 Linear Programming Spring 2007...

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