Reaction Product Reactant requirements (kg) per kg product 0.6 A; 0.4 B 0.4 A; 0.5 B;...

   

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Reaction Product Reactant requirements (kg) per kg product 0.6 A; 0.4 B 0.4 A; 0.5 B; 0.1 C m A; n B; p C I || ||| Table 2: Reaction cost and price of each product Reaction cost Product price D E F Chemical Batch 1 Batch 2 Due to the carelessness a junior manager, the key information regarding the mass conservation of Reaction III is missing. In Table 2, m, n, and p are the amount (weight basis) of reactant A, B, and C, respectively, required to synthesise 1 kg F. In order to retrieve this missing information, a process engineer has made a mass balance using historical data of two recent batches. This is listed in Table 3. 1.5 £/kg D 0.5 £/kg E 1.0 £/kg F Table 3: Mass balance of reactants and products in two previous batch operations Totally consumed reactants (approx.) Totally produced products xc 138 kg 250 kg XA 877 kg 782 kg 783 kg 857 kg 5.0 £/kg D 3.5 £/kg E 4.5 £/kg F XD 1000 kg 500 kg 600 kg 1000 kg XF 200 kg 400 kg 2. Least-squares model construction (5 marks): 2.1. Use only Table 2 and Table 3 to construct a full least-squares model with an objective to calculate m, n, and p. You can only build the model using: x₁,1 (kg day-1 of A consumed in batch 1), XB,1 (kg day¹ of B consumed in batch 1), xc.1 (kg day-¹ of C consumed in batch 1), XA2 (kg day¹ of A consumed in batch 2), x8,2 (kg day-¹ of B consumed in batch 2), xcz (kg day¹ of C consumed in batch 2), m, n, and p. No other symbols are allowed to use. The full model should consist of both an objective function and all possible constraints - remember that all constraints, as well as the objective function, should be independent from each other. Note: Do not use the 'normalised least-squares objective function. 2.2. Restructure the full optimisation model in 2.1 into a reduced optimisation model by substituting the equality constraints where appropriate. Make sure the reduced model only consists of inequality constraints. The reduced model should consist of both an objective function and all possible inequality constraints. Note: Do not use the 'normalised' least-squares objective function. Reaction Product Reactant requirements (kg) per kg product 0.6 A; 0.4 B 0.4 A; 0.5 B; 0.1 C m A; n B; p C I || ||| Table 2: Reaction cost and price of each product Reaction cost Product price D E F Chemical Batch 1 Batch 2 Due to the carelessness a junior manager, the key information regarding the mass conservation of Reaction III is missing. In Table 2, m, n, and p are the amount (weight basis) of reactant A, B, and C, respectively, required to synthesise 1 kg F. In order to retrieve this missing information, a process engineer has made a mass balance using historical data of two recent batches. This is listed in Table 3. 1.5 £/kg D 0.5 £/kg E 1.0 £/kg F Table 3: Mass balance of reactants and products in two previous batch operations Totally consumed reactants (approx.) Totally produced products xc 138 kg 250 kg XA 877 kg 782 kg 783 kg 857 kg 5.0 £/kg D 3.5 £/kg E 4.5 £/kg F XD 1000 kg 500 kg 600 kg 1000 kg XF 200 kg 400 kg 2. Least-squares model construction (5 marks): 2.1. Use only Table 2 and Table 3 to construct a full least-squares model with an objective to calculate m, n, and p. You can only build the model using: x₁,1 (kg day-1 of A consumed in batch 1), XB,1 (kg day¹ of B consumed in batch 1), xc.1 (kg day-¹ of C consumed in batch 1), XA2 (kg day¹ of A consumed in batch 2), x8,2 (kg day-¹ of B consumed in batch 2), xcz (kg day¹ of C consumed in batch 2), m, n, and p. No other symbols are allowed to use. The full model should consist of both an objective function and all possible constraints - remember that all constraints, as well as the objective function, should be independent from each other. Note: Do not use the 'normalised least-squares objective function. 2.2. Restructure the full optimisation model in 2.1 into a reduced optimisation model by substituting the equality constraints where appropriate. Make sure the reduced model only consists of inequality constraints. The reduced model should consist of both an objective function and all possible inequality constraints. Note: Do not use the 'normalised' least-squares objective function.

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