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Linear Programming Models in Services

Linear Programming Models in Services. Stereo Warehouse. Let x = number of receivers to stock y = number of speakers to stock Maximize 50x + 20y gross profit Subject to 2x + 4y 400 floor space 100x + 50y 8000 budget

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Linear Programming Models in Services

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  1. Linear Programming Models in Services

  2. Stereo Warehouse Let x = number of receivers to stock y = number of speakers to stock Maximize 50x + 20y gross profit Subject to 2x + 4y 400 floor space 100x + 50y 8000 budget x 60 sales limit x, y 0

  3. Graphical SolutionStereo Warehouse Z=3800 Z=3600 Z=3000 Z=2000 E Optimal solution ( x = 60, y = 40) D C A B

  4. Model in Standard Form Let s1 = square feet of floor space not used s2 = dollars of budget not allocated s3 = number of receivers that could have been sold Maximize Z = 50x + 20y subject to 2x + 4y + s1 = 400 (constraint 1) 100x + 50y + s2 = 8000 (constraint 2) x + s3 = 60 ( constraint 3) x, y, s1, s2, s3 0

  5. Stereo WarehouseExtreme-Point Solutions Extreme Nonbasic Basic Variable Objective-function point variables variables value value Z A x, y s1 400 0 s2 8000 s3 60 B s3, y s1 280 3000 s2 2000 x 60 C s3, s2 s1 120 3800 y 40 x 60 D s1, s2 s3 20 3600 y 80 x 40 E s1, x s3 60 2000 y 100 s2 3000

  6. Sensitivity AnalysisObjective-Function Coefficients z = 50x + 20y (constraint 3 ) D (constraint 1) (constraint 2) C A B

  7. Sensitivity AnalysisRight-Hand-Side Ranging (constraint 3 ) D H (constraint 2) C A B I

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