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co227_a3

# co227_a3 - and if so ﬁnd a feasible basis(a maximize 22 x...

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Assignment 3 Due: Wednesday October 26 at the BEGINNING of class 1. Given the following linear programs with feasible basis B , do the following: (i) solve the linear program without tableau, give an appropriate certificate (ii) solve the linear program with tableau (a) maximize 2 x 1 - x 2 - x 3 + 3 x 4 + x 5 - x 6 subject to x 1 + x 2 + x 4 + x 5 - 2 x 6 = 3 - x 1 + x 2 - 2 x 3 + 2 x 5 + x 6 = 2 x 1 - x 2 + x 3 + x 4 - x 5 = 1 x 1 , x 2 , x 3 , x 4 , x 5 , x 6 0 Basis B = { 1 , 2 , 6 } (b) maximize x 1 - 3 x 2 + 2 x 3 + 2 x 4 + x 5 + 3 x 6 subject to x 1 + 2 x 2 - 2 x 3 + x 4 + 2 x 6 = 5 x 1 - x 3 + x 4 - x 5 = 4 - x 1 + x 2 + x 3 + 2 x 4 - x 5 + 2 x 6 = 9 x 1 , x 2 , x 3 , x 4 , x 5 , x 6 0 Basis B = { 2 , 4 , 6 } 2. For the following linear programs, use an auxiliary LP to determine if it is feasible,
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Unformatted text preview: and if so ﬁnd a feasible basis. (a) maximize 22 x 1 + 37 x 2-x 3-50 x 4 + 4 x 5 subject to 3 x 1-x 2 + 4 x 3 + x 4 + 5 x 5 = 3 2 x 1 + 3 x 3-2 x 4 + x 5 = 4 x 1 + x 2 + 2 x 3 + 4 x 5 = 1 x 1 ,x 2 ,x 3 ,x 4 ,x 5 ≥ (b) maximize 2 x 1 + x 2-x 3 + 4 x 4 + x 5 subject to x 1 + 2 x 2 + 2 x 4 + x 5 = 2 x 1 + 3 x 2 + 2 x 3 + 2 x 5 = 9 3 x 1 + x 2 + x 3 + 2 x 4-x 5 = 4 x 1 ,x 2 ,x 3 ,x 4 ,x 5 ≥...
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