HW4Solution

# HW4Solution - Introduction to Mathematical Programming IEOR...

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Introduction to Mathematical Programming 833 Mudd IEOR 3606, Prof. Maria Chudnovky Tu&Th 2:40 – 3:55 1 HOMEWORK 4- SOLUTIO& 29-09-2008 1. EXERCISE 1 P. 301 P1 Find the dual of the following LP; Primal: 0 , 4 2 3 1 . 2 max 2 1 2 1 2 2 1 2 1 + + + = x x x x x x x x t s x x z Dual 0 , 1 2 2 . 4 3 min 2 1 3 2 1 3 2 1 3 2 1 + + + + + = y y y y y y y y t s y y y v 2. EXERCISE 2 P.301 P2 Find the dual of the following LP: 0 , 3 2 1 4 2 . min 2 1 2 1 2 1 2 1 2 1 + + + = y y y y y y y y t s y y w First we find the max equivalent problem:

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Introduction to Mathematical Programming 833 Mudd IEOR 3606, Prof. Maria Chudnovky Tu&Th 2:40 – 3:55 2 0 , 3 2 1 4 2 . max 2 1 2 1 2 1 2 1 2 1 + = y y y y y y y y t s y y w Then the dual is: 0 , 1 2 1 2 . 3 4 min 2 1 3 2 1 3 2 1 3 2 1 = x x x x x x x x t s x x x v 3. EXERCISE 3 Suppose we are working with a min problem and increase the right hand side of a
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## HW4Solution - Introduction to Mathematical Programming IEOR...

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