Quantitative Models:
Quantitative Models
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LINEAR PROGRAMMING Mathematical method for helping to determine ways to achieve the best results in a company Technique to optimize
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MINIMIZE MAXIMIZE
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COMPONENTS OF THE MATHEMATICAL MODEL : Objective function Constraint
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Vector of costs
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Soldiers Trains Cost (Material) Cost ( Man Power ) Process 1 ( hours ) Process 2 ( hours ) 1000 1400 1 h 2 h 2700 900 1000 1 h 1 h 2100 Selling price 80 h 100 h Profit per soldier = 2700-1000-1400=300 Profit per train = 2100-900-1000 =200
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Objective Function = Max Z(x)= 300X1+200X2 Subject to X1+X2 <=80 2X1+X2<=100 X1 <=40 X1, X2 >=0
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Vertex X1 X2 Z(X)= 300X1+200X2 A 0 0 0 B 40 0 12000 C 40 20 16000 D 20 60 18000 E 0 80 16000