# Example: Advertising with HIM/LIP/HIW and Budget constraints # with(LinearAlgebra): interface(rtablesize=11);

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# Vars: x1 x2 s1 e1 s2 e2 s3 e3 s4 (and rhs) A:=<<0,7,10,5,100>|<0,3,5,4,60>|<50,1,0,0,0>|<0,-1,0,0,0>|<100,0,1,0,0>|<0,0,-1,0,0>|<200,0,0,1,0>|<0,0,0,-1,0>|<0,0,0,0,1>|<1,0,0,0,-1>|<0,40,60,35,600>>;

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# Clear the values above the identity columns for an initial BFS: A2:=RowOperation(A,[1,2],-50): A3:=RowOperation(A2,[1,3],-100): A4:=RowOperation(A3,[1,4],-200);

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# Pivot in Column 1, and perform Ratio Test: evalf([40/7, 60/10, 35/5, 600/100]);

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#Pivot in Column 1, Row 2: A5:=RowOperation(A4,2,1/7): A6:=RowOperation(A5,[1,2],2350): A7:=RowOperation(A6,[3,2],-10): A8:=RowOperation(A7,[4,2],-5): A9:=RowOperation(A8,[5,2],-100);

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# Pivot in Column 2, and perform Ratio Test: Last row evalf([(40/7)/(3/7), (20/7)/(5/7), (45/7)/(13/7), (200/7)/(120/7)]);

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A10:=RowOperation(A9,5,7/120): A11:=RowOperation(A10,[1,5],3100/7): A12:=RowOperation(A11,[2,5],-3/7): A13:=RowOperation(A12,[3,5],-5/7): A14:=RowOperation(A13,[4,5],-13/7);

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evalf( [A14[2,11]/A14[2,3], A14[4,11]/A14[4,3] ]);

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# Pivot in Column 3, Row 4: A15:=RowOperation(A14,4,6/5): A16:=RowOperation(A15,[1,4],100/3): A17:=RowOperation(A16,[2,4],-1/2): A18:=RowOperation(A17,[3,4],5/6): A19:=RowOperation(A18,[5,4],5/6);

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evalf([A19[3,11]/A19[3,10], A19[4,11]/A19[4,10], A19[5,11]/A19[5,10]]);

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# Pivot in Column 10, Row 4 A20:=RowOperation(A19,4,100/13): A21:=RowOperation(A20,[1,4],41/2): A22:=RowOperation(A21,[2,4],1/25): A23:=RowOperation(A22,[3,4],-3/20): A24:=RowOperation(A23,[5,4],-1/20);

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evalf([A24[3,11]/A24[3,4], A24[5,11]/A24[5,4]]);

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# Pivot in Column 4, Row 3 A25:=RowOperation(A24,3,13/15): A26:=RowOperation(A25,[1,3],1400/13): A27:=RowOperation(A26,[2,3],4/13): A28:=RowOperation(A27,[4,3],100/13): A29:=RowOperation(A28,[5,3],-5/13);

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