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Homework9

Homework9 - ENGRI 1101 Engineering Applications of OR Fall...

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ENGRI 1101 Engineering Applications of OR Fall ’09 Homework 9 Linear and Integer Programming: Relaxations Due date: 4:00pm on Friday, November 13, 2009 in the ENGRI 1101 box at the west end of the corridor on the second floor of Rhodes Hall, where it connects to Upson. Reading assignment: Chapter 3 of Winston, Chapter 2 of Chvatal and section on The Duality Theorem (included in coursepack). Make sure to put your name, netid, and section on the first page and staple the problems in order. 1. (40 points) There are n retail outlets to be furnished with inventory; retail outlet j has a demand for d j units, j = 1 , . . . , n . The distributer is trying to decide at which of the n outlets to build distribution centers. (At least one center must be built, but otherwise, there is no explicit constraint on the number that may be built.) At outlet j = 1 , . . . , n , it would cost f j dollars to build a distribution center. For each retail outlet j = 1 , . . . , n there is one distribution center from which it gets all of its units of demand. (Of course, one outlet may get (all of its) units from a center located at outlet 5, whereas another outlet may get (all of its) units from a center located at outlet 17. If an outlet j get its units from a center at i , then it costs c ij dollars to supply each unit (and so the

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