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Unformatted text preview: . 000001 .) (c) (10 points) ³or what values of ε is the solution you found in ( b ) feasible? (d) (10 points) ³or what values of ε is the solution you found in ( b ) optimal? 2. (40 points) In the previous question you solved the following LP: maximize 3 x 1 + 2 x 2 + 4 x 3 subject to x 1 + x 2 + 2 x 3 ≤ 4 2 x 1 + 3 x 3 ≤ 5 2 x 1 + x 2 + 3 x 3 ≤ 7 x 1 , x 2 , x 3 ≥ . The dual of this poblem is: minimize 4 y 1 + 5 y 2 + 7 y 3 subject to y 1 + 2 y 2 + 2 y 3 ≥ 3 y 1 + y 3 ≥ 2 2 y 1 + 3 y 2 + 3 y 3 ≥ 4 y 1 , y 2 , y 3 ≥ . 1 (a) (25 points) Now take the dual of the dual problem (Frst transform it into canonical form, then take the dual). Transform your answer, if necessary, into canonical form. (b) (15 points) Recall how we derived the dual, by considering how to construct upper bounds on the objective value of the primal. Can you explain your result of ( a ) in this light? 2...
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 '05
 TROTTER
 Linear Programming, Optimization, Dual problem, Duality, Rhodes Hall

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