ps1 - Homework 1 IE418 Discrete Optimization Dr. Ralphs Due...

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Homework 1 IE418 – Discrete Optimization Dr. Ralphs Due January 30, 2007 1. A company has obtained permission to opencast mine within a square plot 200 ft X 200 ft. The angle of slip of the soil is such that it is not possible for the sides of the excavation to be steeper than 45 . The company has obtained estimates for the value of the ore in various places at various depths. Bearing in mind the restrictions imposed by the angle of slip, the company decides to consider the problem as one of extracting rectangular blocks. Each block has horizontal dimensions 50 ft X 50 ft and a vertical dimension of 25 ft. If the blocks are chosen to lie above one another, then it is only possible to excavate blocks forming an upturned pyramid. The following four diagrams show the percentage of pure metal in each of the blocks within the maximum pyramid that can be extracted. 1.5 1.5 1.5 0.75 1.5 2.0 1.5 0.75 1.0 1.0 0.75 0.5 0.75 0.75 0.5 0.25 Level 1 (surface) 4.0 4.0 2.0 3.0 3.0 1.0 2.0 2.0 0.5

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ps1 - Homework 1 IE418 Discrete Optimization Dr. Ralphs Due...

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