# Example: Advertising with HIM/LIP/HIW and Budget constraints # This uses the penalties and budget as a goal. with(LinearAlgebra): interface(rtablesize=11); # Vars: x1 x2 s1m s1p s2m s2p s3m s3p s4m s4p (and rhs) A:=<<0,7,10,5,100>|<0,3,5,4,60>|<200,1,0,0,0>|<0,-1,0,0,0>|<100,0,1,0,0>|<0,0,-1,0,0>|<50,0,0,1,0>|<0,0,0,-1,0>|<0,0,0,0,1>|<1,0,0,0,-1>|<0,40,60,35,600>>; # Clear the values above the identity columns for an initial BFS: A2:=RowOperation(A,[1,2],-200): A3:=RowOperation(A2,[1,3],-100): A4:=RowOperation(A3,[1,4],-50); # Pivot in Column 1, and perform Ratio Test: evalf([40/7, 60/10, 35/5, 600/100]); #Pivot in Column 1, Row 2: A5:=RowOperation(A4,2,1/7): A6:=RowOperation(A5,[1,2],2650): A7:=RowOperation(A6,[3,2],-10): A8:=RowOperation(A7,[4,2],-5): A9:=RowOperation(A8,[5,2],-100); # Pivot in Column 4, and perform Ratio Test: Tie between 3 and 5. Choose 3: A10:=RowOperation(A9,3,7/10): A11:=RowOperation(A10,[1,3],1250/7): A12:=RowOperation(A11,[2,3],1/7): A13:=RowOperation(A12,[4,3],-5/7): A14:=RowOperation(A13,[5,3],-100/7); # Pivot in Column 2, Row 5: A15:=RowOperation(A14,5,1/10): A16:=RowOperation(A15,[1,5],75): A17:=RowOperation(A16,[2,5],-1/2): A18:=RowOperation(A17,[4,5],-3/2): A19:=RowOperation(A18,[3,5],-1/2); # Pivot in Column 10, Row 4: A20:=RowOperation(A19,4,20/3): A21:=RowOperation(A20,[1,4],13/2): A22:=RowOperation(A21,[2,4],-1/20): A23:=RowOperation(A22,[3,4],-1/20): A24:=RowOperation(A23,[5,4],1/10); # Optimal Tableau!