This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Fall 2009 IEOR 160 Industrial Engineering & Operations Research October 22, 2009 Page 1 of 2 HOMEWORK 7 SOLUTIONS Section 12.9 2. KT conditions yield (1) 1 2 x 1 = 0 (2) 1 2 x 2 = 0 (3) (1 x 2 1 x 2 2 ) = 0 , 0. Trying > 0, we find from (1) and (2) that x 1 = 1 2 and x 2 = 1 2 . Then (3) yields = 2 2 . Finally we find that x 1 = x 2 = 2 2 . Since the constraint is convex and the objective function is linear, we know that we have found an optimal solution to the problem. 5. Let L 1 be the labor purchased at $15 per hour and L 2 the aabor purchased at $25 per hour. We wish to solve max 270( L 1 + L 2 ) 1 / 2 K 1 / 3 15 L 1 25 L 2 5 K subject to L 1 160 and all variables nonnegative. Ignoring the nonnegativity restrictions, the KT conditions yield (1) 135( L 1 + L 2 ) 1 / 2 K 1 / 3 15 = 0 (2) 135( L 1 + L 2 ) 1 / 2 K 1 / 3 25 = 0 (3) 90( L 1 + L 2 ) 1 / 2 K 2 / 3 5 = 0 (4) (160 L 1 ) = 0, 0....
View
Full
Document
 Fall '07
 HOCHBAUM
 Operations Research

Click to edit the document details