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Unformatted text preview: Assignment 1 Due: Wednesday September 28 at the BEGINNING of class 1. Pat’s Porsches is a local company that makes cars that look like Porsches. There are 2 suppliers (S1,S2) that provide the steel to make the cars. Each supplier can supply the following amounts this year at the following prices: Supplier max tons available price/ton (in $) S1 50 10000 S2 86 13000 The company has 3 plants (P1,P2,P3) that make the cheap cars. There is a cost to ship each ton of steel from each supplier to the plants (in $): P1 P2 P3 S1 42 45 37 S2 35 44 38 Each plant has a maximum amount of cars they can produce in a year and different labour costs: P1 P2 P3 Max cars can produce 40 50 45 Labour Cost ($ per car) 2000 1750 2100 Each car takes 1 ton of steel to make. The cars are sold for $30,000 each. With prices so low, they are selling off faster than they can make them. Write a mathematical program to maximize the profit for the company this year. Solution: Let x ij denote the amount of steel (in tons) from supplier i to plant j . maximize 30 , 000 2 X i =1 3 X j =1 x ij [10000( 3 X j =1 x 1 j ) + 13000( 3 X j =1 x 2 j )] [42 x 11 + 45 x 12 + 37 x 13 + 35 x 21 + 44 x 22 + 38 x 23 ] [2000( x 11 + x 21 ) + 1750( x 12 + x 22 ) + 2100( x 13 + x 23 )] subject to...
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 Fall '10
 1
 Optimization, raw material, mathematical program

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