Hw9s - ENGRI 1101 Engineering Applications of OR Fall 08...

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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...
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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).

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Hw9s - ENGRI 1101 Engineering Applications of OR Fall 08...

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