DMOR-05-06 - UF-ESI-6314 Problem Statement page 1 of 4...

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UF-ESI-6314 3a360f4b5747f496085a91e86bb1e0ade081dc59.xls Problem Statement page 1 of 4 Luther Setzer 1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899 (321) 544-7435 Maximize subject to 05-06. Solve the following problem by branch-and-bound. Solve the linear programming problems at each node of your branch-and-bound tree graphically (and please show your work). 5 x 1 + 2 x 2 x 1 + x 2 8 3 x 1 + 2 x 2 16 x ≥ 0 and integer
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UF-ESI-6314 3a360f4b5747f496085a91e86bb1e0ade081dc59.xls Relaxed Solution page 2 of 4 Luther Setzer 1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899 (321) 544-7435 Begin by graphing the given linear program and solving in a relaxed fashion. ==> ==> Series 1 Series 2 0 8 8 16 16 1 7 6 1/2 19 18 2 6 5 22 20 3 5 3 1/2 25 22 4 4 2 28 24 5 3 1/2 31 26 5 1/3 2 2/3 0 32 26 2/3 6 2 -1 34 28 7 1 -2 1/2 37 30 8 0 -4 40 32 Solving graphically shows Series 1 as outside the feasible region and yields: = 5 1/3 = 0 z = 26 2/3 z = 5 x 1 + 2 x 2 x 1 + x 2 8 x 2 8 - x 1 3 x 1 + 2 x 2 16 x 2 8 - 3/2( x 1 ) x ≥ 0 x 1 x 2 x 2 z 1 z 2 x 1 x 2 0 1 2 3 4 5 6 7 8 9 -6 -4 -2 0 2 4 6 8 10 Column B Column C x1 x2
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