2. Find the dual to the following standard minimum problem. Find yl , y2 and y3 tominimize yl + 2y2+y3 , subject to the constraints, yi 20 for all i, andyl – 2y2 + y3 22-yl + y2 + y3 242yl + y3 26yl + y2 + y3 2 2.3. Consider the problem of question 2. Show that (yl, y2, y3) = (2/3, 0, 14/3) isoptimal for this problem, and that (x1, x2, x3, x4) = (0, 1/3, 2/3, 0) is optimal for the dual.

If the primal problem is of the form Minimize z=CY Subject to AY>=b Y>=0 Then it's dual…

2. Find the dual to the following standard minimum problem. Find yl , y2 and y3 to minimize yl + 2y2+ y3 , subject to the constraints, yi 20 for all i, and yl – 2y2 + y3 22 -yl + y2 + y3 24 2y1 + y3 26 yl + y2 + y3 22. 3. Consider the problem of question 2. Show that (yl, y2, y3) = (2/3, 0, 14/3) is optimal for this problem, and that (x1, x2, x3, x4) = (0, 13, 2/3, 0) is optimal for the dual.

2. Find the dual to the following standard minimum problem. Find yl , y2 and y3 to minimize yl + 2y2+ y3 , subject to the constraints, yi 20 for all i, and yl – 2y2 + y3 22 -yl + y2 + y3 24 2y1 + y3 26 yl + y2 + y3 22. 3. Consider the problem of question 2. Show that (yl, y2, y3) = (2/3, 0, 14/3) is optimal for this problem, and that (x1, x2, x3, x4) = (0, 13, 2/3, 0) is optimal for the dual.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 17EQ

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