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Final_Solution

Final_Solution - CS570 FALL 2006 FINAL SOLUTION Problem 1...

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CS570 FALL 2006 FINAL SOLUTION Problem 1: 1.True 2.True 3.False 4.False 5.True 6.True 7.False 8.Unknown 9.True 10.True Problem 2: Solution 1): Assume that the weight of material 1, material 2 and material 3 carried on the cargo plane are x 1 , x 2 and x 3 respectively. Clearly x 1 0 , x 2 0 , x 3 0. Then the total revenue is 1000 * x 1 / 2+1200 * x 2 / 1+12000 * x 3 / 3. As the cargo plane can carry a maximum of 100 tons and a maximum of 60 cubic meters of cargo, we have x 1 + x 2 + x 3 100, x 1 / 2 + x 2 / 1 + x 3 / 3 60; As Material 1 has maximum available amount 40 cubic meters, we have x 1 / 2 40;As Material 2 has maximum available amount 30 cubic meters, we have x 2 / 1 30; As Material 3 has maximum available amount 20 cubic meters, we have x 3 / 3 20; Hence the linear program which optimize revenue is: max(1000 * x 1 / 2 + 1200 * x 2 / 1 + 12000 * x 3 / 3) subject to: x 1 0 , x 2 0 , x 3 0 , x 1 + x 2 + x 3 100 , x 1 / 2 + x 2 / 1 + x 3 / 3 60 , x 1 / 2 40 , x 2 / 1 30 , x 3 / 3 20 . Solution 2): Assume that the amount of material 1, material 2 and material 3 carried on the cargo plane are x 1 , x 2 and x 3 respectively. Clearly x 1 0 , x 2 0 , x 3 0. Then the total revenue is 1000 * x 1 + 1200 * x 2 + 12000 * x 3 . As the cargo plane can carry a maximum of 100 tons and a maximum of 60 cubic meters of cargo, we have x 1 + x 2 + x 3 60, x 1 * 2 + x
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