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: ENGRI 1101 Engineering Applications of OR Fall 08 Homework 9 Homework 9 Solutions 1. (a) In this problem the initial feasible dictionary is: x 4 = 4 x 1 x 2 2 x 3 x 5 = 5 2 x 1 3 x 3 x 6 = 7 2 x 1 x 2 3 x 3 z = 3 x 1 +2 x 2 +4 x 3 Now we want to increase the objective value, z . In this case, increasing any of x 1 , x 2 , x 3 would increase the value of z . We arbitrarily choose x 1 . Examining the upper bounds imposed by the constraints x 4 , x 5 , x 6 0, we find x 5 0 to be most stringent, which implies x 1 2 . 5. From the second equation in the previous dictionary we have x 1 = 2 . 5 1 . 5 x 3 . 5 x 5 and substituing it into the previous dictionary we arrive at a new dictionary with increased optimal value: x 4 = 1 . 5 x 2 . 5 x 3 +0 . 5 x 5 x 1 = 2 . 5 1 . 5 x 3 . 5 x 5 x 6 = 2 x 2 + x 5 z = 7 . 5 +2 x 2 . 5 x 3 1 . 5 x 5 Now we can only choose to increase x 2 to increase z . Of all the constraints, x 4 0 limits the increase of x 2 the most (making x 2 1 . 5). From the first equation in the previous dictionary we have x 2 = 1 . 5 . 5 x 3 x 4 + 0 . 5 x 5 and substituting it into the previous dictionary we arrive at a new dictionary with increased optimal value: x 2 = 1 . 5 . 5...
View
Full
Document
This note was uploaded on 11/12/2009 for the course ENGRD 2700 taught by Professor Staff during the Spring '05 term at Cornell University (Engineering School).
 Spring '05
 STAFF

Click to edit the document details