Nature research paper: Crop switching can enhance environmental sustainability and farmer incomes in China
G2 : assigns priority to one sustainability dimension while not degrading outcomes for the other sustainability dimensions.$${\sum }_{\{{\rm{irr,ra}}\},i,j}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}\cdot {{\rm{YLD}}}_{{\rm{irr/ra}},i,z}\ge {\sum }_{\{{\rm{irr,ra}}\}}{{\rm{Production}}}_{{\rm{Cur,irr/ra}},z}$$
$${\sum }_{\{{\rm{irr,ra}}\},i,j,z}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}\cdot {{\rm{GW}}}_{i,z}\le {\sum }_{\{{\rm{irr,ra}}\},i}{{\rm{TGW}}}_{{\rm{irr/ra}},i}$$ $${\sum }_{\{{\rm{irr,ra}}\},i,j,z}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}\cdot {{\rm{FP}}}_{i,z}\le {\sum }_{\{{\rm{irr,ra}}\},i}{{\rm{TFP}}}_{{\rm{irr/ra}},i}$$
$${\sum }_{\{{\rm{irr,ra}}\},j,z}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}\cdot {{\rm{YLD}}}_{{\rm{irr/ra}},i,z}\cdot {{\rm{NetProfit}}}_{i,z}\ge {\sum }_{\{{\rm{irr,ra}}\}}{{\rm{TFI}}}_{{\rm{irr/ra}},i}$$ $${\sum }_{\{{\rm{irr,ra}}\},j,z}{{\rm{CA}}}_{{\rm{irr/ra}},i}\cdot {x}_{{\rm{irr/ra}},i,j}\cdot {R}_{j,z}\cdot {{\rm{FN}}}_{i,z}\le \left\{\begin{array}{l}{\sum }_{\{{\rm{irr,ra}}\}}{{\rm{TFN}}}_{{\rm{irr/ra}},i}| \\ {{\rm{UPBOUND}}}_{{\rm{N}},i}| \end{array}\right.$$
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