HW3_soln - 3.4.1. Factory 1 2 3 Process Cost ($/ton) 15 10...

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3.4.1 . Factory Process Cost ($/ton) Reduction Waste 1 Waste 2 1 15 0.1 0.45 2 10 0.2 0.25 3 20 0.4 0.3 Requirements: reduce pollutant 1 by at least 30 tons Reduce pollutant 3 by at least 40 tons Variables: For i = 1, 2, 3 let x i = Tons of processed Factory i waste. Then appropriate LP is min z = 15x 1 + 10x 2 + 20x 3 s.t. .10x 1 + .20x 2 + .40x 3 30(Pollutant 1) .45x 1 + .25x 2 + .30x 3 40(Pollutant 2) x 1 0, x 2 0, x 3 0 The following assumptions are reasonable because: Proportionality: - cost of processing from each factory contributes to the total cost linearly - amount of pollutant reduced in each factory should contribute linearly to the total pollutant reduction i.e. no terms like 2 i x , where i = 1, 2, 3 Additivity: - cost of processing in each factory should be independent of each other - amount of pollution reduction in each factory should be independent of each other i.e. no terms like 12 x x Divisibility: - amount of waste can take on fractional values Certainty : - we are given deterministic data. No stochastic data
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3.4.3 (a). Let x1 = units of food 1 bought and x2 = units of food 2 bought. Then we wish to solve
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HW3_soln - 3.4.1. Factory 1 2 3 Process Cost ($/ton) 15 10...

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