IE301-HW3_2009-2010 - ATILIMUNIVERSITY...

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ATILIM UNIVERSITY DEPARTMENT OF INDUSTRIAL ENGINEERING IE 301 OPERATİONS RESEARCH I ( Fall 2009 ) Homework # 3                                                  (Due  13/11/2009) 1. (25 Points) Consider the following problem. Maximize Z = x 1 + x 2 +x 3 + x 4 Subject to x 1 + x 2 ≤ 3 x 3 + x 4 ≤ 2 and x j ≥ 0, for j = 1, 2, 3, 4. Work through the simplex method step by step to find all the optimal BF solutions. 2. (25 Points) Solve the following LP problem using the BIG-M Simplex method. Show your work clearly. Maximize Z = 3x 1 + 5x 2 Subject to x 1 4 2x 2 ≤ 12 3x 1 + 2x 2 = 18 x 1 ≥ 0 and x 2 ≥ 0 3. (25 Points) Use the TWO-PHASE simplex method to solve the following LP problem. Show your work clearly. Minimize Z = 0.4x 1 + 0.5x 2 Subject to 0.3x 1 + 0.1x 2 ≤ 2.7 0.5x 1 + 0.5x 2 = 6 0.6x 1 + 0.4x 2 ≥ 6 x 1 ≥ 0 and x 2 ≥ 0 4.(25 Points) A production manager must decide on the mix of products to produce for the
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IE301-HW3_2009-2010 - ATILIMUNIVERSITY...

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