Question 4 (20 pts) In mining operations, one of the most important problems is

Question

Question 4 (20 pts) In mining operations, one of the most important problems is to determine the best contour of an open-pit mine. In an open-pit mine, the mined region is divided into blocks on various levels. Depending on the geography of the mine and the technology used, restrictions are imposed on how the blocks can be accessed. For example, consider the mine given in figure below consisting of three levels 1236 9 10 11 12 13 14 15 Figure. Open pit mine example In this setup, a block cannot be removed and accessed unless the blocks immediately above it and to its right and left are removed; for example, block 10 cannot be accessed unless blocks 3, 4, and 5 are removed, while block 13 requires blocks 8, 9, and 10 to be removed. Suppose that, in the example above, we are trying to extract a precious ore from this mine Based on the results of test drillings, it has been determined that blocks 3, 5, 9, 10, 12, and 15 contain the desired ore. The amount of ore in each of these blocks varies, so that their market value (per ton) is given in the following table 3 59 0 12 15 Block Value of ore (per ton) $300 $800 S600 S1000 $600 $1300 Suppose that it costs S 200 per ton to remove a block in the top level, S 350 per ton in the middle level, and S 600 per ton in the bottom level. Formulate an integer program which determines the blocks that should be extracted to maximize the profit margin

Explanation / Answer

3,4,5,10 excavation-per tonn profit will be $1150,then 6,7,11,12,15 excavation - 200,;2,9 excavation profit-50

So total profit -1400

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