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Unformatted text preview: s.t. x 1 + 5 x 2 + 2 x 3 = 30 x 15 x 26 x 3 ≤ 40 x 1 ,x 2 ,x 3 ≥ Let x 4 be the artiﬁcial variable of the ﬁrst constraint and x 5 be the slack variable of the second constraint. Both variables are the starting basic variables for the implementation of the bigM method. The partial optimal simplex tableau is given as follows: basic x 1 x 2 x 3 x 4 x 5 Solution ¯ c 23 7 (5 + M ) 150 x 1 1 x 5 1 (a) Write the associated dual problem and determine its optimal solution from the above tableau. (b) Complete the optimal tableau. 5. Consider the following primal LP problem: min 6 x 15 x 3 s.t. 6 x 13 x 2 + x 3 = 2 3 x 1 + 4 x 2 + x 3 ≤ 5 x 17 x 2 ≤ 5 x 1 ≥ ,x 2 ≤ . (a) Write the dual of the above linear programming problem. (b) Use the Complementary Slackness Theorem to check whether the solution ( x 1 ,x 2 ,x 3 ) = (0 , , 2) is an optimal solution. 2...
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 Spring '10
 TanBanPin
 Linear Programming, Optimization, Dual problem, linear programming problem, National University of Singapore, Department of Mathematics

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