exam1review

# exam1review - Exam 1 Review IE 220 Fall 2006 October 3,...

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Exam 1 Review IE 220 Fall 2006 October 3, 2006

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Exam 1 Review Problem 1 Problem 1 Consider the following LP: maximize Z = x 1 + 2 x 2 subject to - x 1 + x 2 4 x 1 - 2 x 2 2 4 x 1 + a x 2 16 x 1 , x 2 0 x 1 x 2 1 5 3 246 7 1 3 4 2 6 5 7 8 9 8 10 x 1 + x 2 =4 x 1 2 x 2 =2 Z Exam 1 Review 2
Exam 1 Review Problem 1 Problem 1, cont’d (a) Find a value of a such that there is a single optimal solution. (b) Find a value of a such that there are an inﬁnite number of optimal solutions. (c) Find a value of a such that the problem is feasible but there are no optimal solutions. Exam 1 Review 3

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Exam 1 Review Problem 1 Problem 1, cont’d (d) Let a = 0. The problem can be written in augmented form as: maximize Z = x 1 + 2 x 2 subject to - x 1 + x 2 + x 3 = 4 x 1 - 2 x 2 + x 4 = 2 4 x 1 + x 5 = 16 x 1 , x 2 , x 3 , x 4 , x 5 0 Let x B = { 4 , 1 , 7 , 0 , 0 } . (i) Is this a basic solution? (ii) Is it a BF solution? (iii) Interpret the values of the slack variables with respect to the location of the point on the feasible region.
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## This note was uploaded on 04/07/2008 for the course IE 220 taught by Professor Storer during the Spring '07 term at Lehigh University .

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exam1review - Exam 1 Review IE 220 Fall 2006 October 3,...

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