A Remys' Company produces two types of product, A (X) and B (X). The production consists...

 

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A Remys' Company produces two types of product, A (X₁) and B (X₂). The production consists of two processes, assembly and finishing. After that, the finished products will be transferred to the store. The company wishes to know the quantity of production in order to maximize the profit and this problem can be expressed as LP model below: Maximize Profit = 30X₁ + 70X2 Subject to Basic Variables X₂ S₂ 4 X₁ + 10 X2 14 X₁ + 8 X₂ X₁ + X₁ Hence, the FINAL tableau for Remys' Company problem would be: X₁, X2 ≥ 0 Ci < 80 < 112 X₂ < 10 70 0 30 Zi Ci-Zi (Assembly in hours unit) (Finishing in hours unit) (Store in meter sq unit) 30 70 X₁ X₂ 0 1 0 0 1 30 0 0 70 0 0 S₁ 1/6 1 0 S₂ 0 20/3 -20/3 1 -1/6 0 5/3 0 0 S3 -2/3 0 -18 10/3 -10/3 Quantity 20/3 12 10/3 566.67 a) Formulate the Dual LP model. b) What are the dual values for this problem? c) If there is/are dual price(s) with zero value? Explain the reason of zero value. d) Let say the company wants to increase the profit of product A (X₁). How much is the maximum increment should be so that the current solution will remain optimal. What is the new profit? A Remys' Company produces two types of product, A (X₁) and B (X₂). The production consists of two processes, assembly and finishing. After that, the finished products will be transferred to the store. The company wishes to know the quantity of production in order to maximize the profit and this problem can be expressed as LP model below: Maximize Profit = 30X₁ + 70X2 Subject to Basic Variables X₂ S₂ 4 X₁ + 10 X2 14 X₁ + 8 X₂ X₁ + X₁ Hence, the FINAL tableau for Remys' Company problem would be: X₁, X2 ≥ 0 Ci < 80 < 112 X₂ < 10 70 0 30 Zi Ci-Zi (Assembly in hours unit) (Finishing in hours unit) (Store in meter sq unit) 30 70 X₁ X₂ 0 1 0 0 1 30 0 0 70 0 0 S₁ 1/6 1 0 S₂ 0 20/3 -20/3 1 -1/6 0 5/3 0 0 S3 -2/3 0 -18 10/3 -10/3 Quantity 20/3 12 10/3 566.67 a) Formulate the Dual LP model. b) What are the dual values for this problem? c) If there is/are dual price(s) with zero value? Explain the reason of zero value. d) Let say the company wants to increase the profit of product A (X₁). How much is the maximum increment should be so that the current solution will remain optimal. What is the new profit?

Answer rating: 100% (QA)

a Dual problem Minimize 80y1 112y2 10y3 st 4y1 14y2 1y3 30 10y1 8y2 1y3 70 y1 y2 y3 0 b The va... View the full answer