This preview shows page 1. Sign up to view the full content.
Unformatted text preview: Consider the following linear program. ( P ) max 2 x 1 + 3 x 2 Subject to x 1 + x 2x 3 + 2 x 4 5 x 2 + 3 x 33 x 4 = 3 x 1 ,x 3 ,x 4 , x 2 free (a) Write the dual (D) of (P). (b) Write the complementary slackness conditions for (P) and (D). (c) Show that, if x is feasible for ( P ) and y is feasible for (D), then x is optimal for ( P ) and y is optimal for (D) if and only if x and y satisfy the complementary slackness conditions. (d) Use the complementary slackness conditions to determine if there is an optimal solution to (P) with x 3 > 0. (e) Use the complementary slackness conditions to determine if there is an optimal solution to (P) with x 1 > 0....
View
Full
Document
 Spring '07
 S.Furino,B.Guenin

Click to edit the document details