hwk6-solution-1

# hwk6-solution-1 - (1)Z-Value(2 Solutions(pt each 1)2 1 1...

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Z-Value (2) (1) pt. each (2) (1) (1) (1) Solutions When there is a big M they have to instantiate the M with a big number so that the package can solve it

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11.3-1 (8 th edition) 1. 11.3-1
X 1 = Production level of Product #1 X 2 = Production level of Product #2 X 3 = Production level of Product #3 X 4 = Production level of Product #4 a) Y 1 = 1 if X 1 > 0; Y 2 = 1 if X 2 > 0; Y 3 = 1 if X 3 > 0; Y 4 = 1 if X 4 > 0; Y 5 = either/or auxiliary binary variable Maximize: Z = 70X 1 – 50,000Y 1 + 60X 2 – 40,000Y 2 + 90X 3 – 70,000Y 3 + 80X 4 – 60,000Y 4 s.t. 1) Y 1 + Y 2 + Y 3 + Y 4 2 ( 2 products can be produced) 2.a) Y 3 Y 1 + Y 2 (Y 3 only if either Y 1 or Y 2 ) 2.b) Y 4 Y 1 + Y 2 (Y 4 only if either Y 1 or Y 2 ) 3.a) 5X 1 + 3X 2 + 6X 3 + 4X 4 6,000 + MY 5 (either 3.a or 3.b holds) 3.b) 4X 1 + 6X 2 + 3X 3 + 5X 4 6,000 + M(1-Y 5 ) (either 3.a or 3.b holds) 4) X 1 MY 1 (Y 1 = 1 when X 1 > 0) 5) X 2 MY 2 (Y 2 = 1 when X 2 > 0) 6) X 3 MY 3 (Y 3 = 1 when X

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hwk6-solution-1 - (1)Z-Value(2 Solutions(pt each 1)2 1 1...

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