Unformatted text preview: (4) Let B be an optimal basis for (P). What is the relation between the optimal dual solution y corre-sponding to B of (P) and the optimal dual solution y corresponding to B of (P’)? Justify your answer! Exercise 3. Let (P) be a linear program and let (D) be its dual. Let x * be a feasible solution for (P) and let y * be a feasible solution for (D). Show that if all variables of (P) and (D) are free (unrestricted) then x * is an optimal solution to (P) and y * is an optimal solution to (D). Exercise 4. Write the dual of the following linear program: max c T x + e T y s.t. Ax + By = b Cx + y ≤ d x ≥ . where A ∈ R m × n ,B ∈ R m × n ,C ∈ R n × n ,c ∈ R n ,e ∈ R n ,b ∈ R m , and d ∈ R n . 1...
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- Winter '07
- Optimization, Diagonal matrix, Constraint, linear program, optimal dual solution