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Unformatted text preview: x = [0 , 3 , , 1] T is feasible to the original linear program. (d) In part (c), we showed that any feasible solution to the original (maximization) problem has to be feasible also to the system ( * ). In particular, it has to solve its ﬁrst equation z + 1 3 x 1 + 1 3 x 3 = 8 which implies (by nonnegativity of x i ’s) z = 81 3 x 11 3 x 3 ≤ 8 . This shows that for any feasible solution to the original problem, the objective value z cannot be larger than 8. On the other hand, as argued in (c), the solution x = [0 , 3 , , 1] is feasible to the original program and attains objective value equal to 8. Hence, it must be optimal to the original problem. 1...
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 Fall '08
 TODD
 Linear Algebra, Optimization, Equals sign, feasible solution, Elementary matrix

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