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examples1 - IE521 Advanced Optimization Example Questions...

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IE521 Advanced Optimization Example Questions Fall 2011 1. Consider a road divided into n segments that is illuminated by m lamps. Let p j be the power of the j th lamp. The illumination I i of the i th segment is assumed to be m j =1 a ij p j where a ij are known coefficients. Let I ? i be the desired illumination of segment i . We are interested in choosing the lamp powers p j so that the illuminations I i are as close as possible to the desired illuminations I ? i . a. Provide a reasonable linear programming formulation of this problem that minimizes the total deviation from the desired level of illuminations. a. Provide a reasonable linear programming formulation of this problem that minimizes the maximum deviation from the desired level of illuminations. 2. A cargo plane has three compartments for storing cargo: front, center, and back. These compartments have capacity limits on both weight and space as summarized below: Compartment Weight Capacity (Tons) Space Capacity (ft 3 ) Front 12 7000 Center 18 9000 Back 10 5000
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