solution1

# solution1 - SL/2901/1/2010 THE UNIVERSITY OF HONG KONG...

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THE UNIVERSITY OF HONG KONG DEPARTMENT OF MATHEMATICS MATH2901 Operations Research I Assignment 1 - Suggested Solution 1.(a) Let x 0 = minimum cost of the renewal planning x 1 = the acres used to build low-income housing. x 2 = the acres used to build middle-income housing. The LP model is: Min 340 , 000 x 1 + 375 , 000 x 2 Subject to x 1 + x 2 10 4 x 1 6 3 x 2 6 4 x 1 + 3 x 2 38 68 x 1 + 75 x 2 500 8 x 1 3 x 2 20 x 1 0 , x 2 0 (b)(i) The canonical form: Max 340 , 000 x 1 375 , 000 x 2 Subject to x 1 + x 2 10 x 1 6 x 1 4 x 2 6 x 2 3 4 x 1 + 3 x 2 38 68 x 1 + 75 x 2 500 8 x 1 + 3 x 2 ≤ − 20 x 1 0 , x 2 0 (ii) The standard form: Min 340 , 000 x 1 + 375 , 000 x 2 Subject to x 1 + x 2 + s 1 = 10 x 1 + s 2 = 6 x 1 s 3 = 4 x 2 + s 4 = 6 x 2 s 5 = 3 4 x 1 + 3 x 2 + s 6 = 38 68 x 1 + 75 x 2 + s 7 = 500 8 x 1 3 x 2 s 8 = 20 x 1 0 , x 2 0 s i 0 , i = 1 , 2 , . . . , 8

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## This note was uploaded on 11/11/2011 for the course MATH MATH2901 taught by Professor Sydneychu during the Fall '11 term at HKU.

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solution1 - SL/2901/1/2010 THE UNIVERSITY OF HONG KONG...

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