Unformatted text preview: max( c T x : Ax = b,x 0) (P) and its dual (D). Let B be a basis of A , let x * be a basic solution for B and let y * := ( A T B )1 c B . (1) Show that x * and y * satisfy the complementary slackness conditions for (P) and (D). (2) Show that c N if and only if y * is feasible for (D). (3) Deduce the (Strong) Duality theorem from (1) and (2). IMPORTANT: You answers should be self contained for part (1) and part (2). Exercise 3. (1) Can the entering variable in one iteration of the simplex method be the leaving variable in the next iteration? (2) Can the leaving variable in one iteration be the entering variable in the next iteration? 1...
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 Spring '07
 S.Furino,B.Guenin
 Linear Programming, Optimization, feasible region, Tutorial Center, following linear program, slack variable x3

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