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Unformatted text preview: + x 4 = 2 4 x 1 + x 23 x 3 + 4 x 4 = 1 2 x 1 + 3 x 22 x 3 = 5 x 1 ,x 2 ,x 3 ,x 4 ≥ r = (1 , 2 , 3 , 4) T , x = (2 , 1 , ,1) T , y = (1 , 2 ,1) T (c) maximize 2 x 1 + x 2 + 4 x 3 subject to 2 x 1x 2 + x 3 = 2x 1 + 2 x 25 x 3 = 2 4 x 1x 2x 3 = 6 x 1 ,x 2 ,x 3 ≥ r = (1 , 3 , 1) T , x = (2 , 2 , 0) T , y = (2 ,1 , 1) T 4. For the following, choose a basis, ﬁnd the corresponding basic solution and improve the solution. (a) maximize x 1x 3 + 4 x 5 subject to 3 x 1 + 5 x 3 + x 4x 5 = 3x 1 + x 32 x 5 + x 6 = 2 x 1 + x 2 + 2 x 3 + 3 x 5 = 3 x 1 ,x 2 ,x 3 ,x 4 ,x 5 ,x 6 ≥ (b) maximizex 1 + 2 x 3 + 4 x 6 subject to x 1 + 4 x 3 + x 5 + x 6 = 4 x 2x 3 + 3 x 6 = 2 2 x 3 + x 42 x 6 = 1 x 1 ,x 2 ,x 3 ,x 4 ,x 5 ,x 6 ≥...
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 Fall '10
 1
 Optimization, linear program, standard equality form

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