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Table 2 CWSR LP model structure in R with decision variables, RHS constraints, and the objective function

From: Time series livestock diet optimization: cost-effective broiler feed substitution using the commodity price spread approach

Objfn1   OB1P1 OB2P1 OB3P1 OB4P1 OB5P1 OB6P1 OB7P1 OB8P1 OB9P1     
Objfn2   OB1P2 OB2P2 OB3P2 OB4P2 OB5P2 OB6P2 OB7P2 OB8P2 OB9P2     
Objfn3      
Objfn4      
Objfn5      
Objfn6      
Objfnn   OB1Pn OB2Pn OB3Pn OB4Pn OB5Pn OB6Pn OB7Pn OB8Pn OB9Pn     
             Constraints
  Item/unit DV1 DV2 DV3 DV4 DV5 DV6 DV7 DV8 DV9   S G F
Constraint W (kg) 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 = 1 1 1
Constraint ME (Mcal/kg) 3.12 3.35 2.44 2.00 8.20 3.61 3.61 0.00 0.00 3.05 3.10 3.15
Constraint Protein (%) 11.50 8.50 48.50 38.00 0.00 57.52 94.40 0.00 0.00 22 20 18
Constraint Calcium (%) 0.05 0.02 0.27 0.68 0.00 0.00 0.00 38.00 22.00 0.95 0.92 0.89
Constraint Available p. (%) 0.00 0.08 0.22 0.30 0.00 0.00 0.00 0.00 18.65 0.475 0.460 0.445
Constraint Arginine (%) 0.40 0.38 3.48 2.08 0.00 0.00 0.00 0.00 0.00 1.377 1.252 1.127
Constraint Lysine (%) 0.31 0.26 2.96 1.94 0.00 0.00 74.42 0.00 0.00 1.148 1.044 0.940
Constraint Meth. Cyst. (%) 0.37 0.36 1.39 1.58 0.00 98.00 0.00 0.00 0.00 0.889 0.808 0.727
Constraint Crude fiber (%) 3.00 2.20 3.90 12.00 0.00 0.00 0.00 0.00 0.00 3 3 3
Upper bound   inf inf inf inf inf inf inf inf inf     
Lower bound   0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00     
  1. Constraints: S denotes the starter diet, G for the grower diet, and F for the finisher diet. Arginin, lysine, and Meth. Cyst. requirements were calculated as proportion of crude protein according to Pesti and Miller (1993)
  2. OB objective function, P1 price decision variable 1, W weight, ME metabolizable energy, P phosphorus, Meth. Cyst. methionine and cysteine, DV decision variable, DV1 wheat grain, DV2 corn grain, DV3 SBM, DV4 RSM, DV5 soybean oil, DV6 DL-methionine, DV7 L-lysine, DV8 limestone, DV9 dicalcium phosphate