# Example 3: Preemptive programming with(LinearAlgebra): interface(rtablesize=11);

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# Vars: x1 x2 e1 e2 e3 s1 s2 s3 (and rhs) A:=<<0,0,0,7,10,5,100>|<0,0,0,3,5,4,60>|<0,0,0,-1,0,0,0>|<0,0,0,0,-1,0,0>|<0,0,0,0,0,-1,0>|<P1,0,0,1,0,0,0>|<0,P2,0,0,1,0,0>|<0,0,P3,0,0,1,0>|<0,0,0,0,0,0,1>|<0,0,0,40,60,35,600>>;

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# A2:=RowOperation(A,[1,4],-P1): A3:=RowOperation(A2,[2,5],-P2): A4:=RowOperation(A3,[3,6],-P3);

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# Work through Priority 1 first (Row 1): Pivot in Column 1 evalf([40/7,60/10,35/5,600/100]);

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# A5:=RowOperation(A4,4,1/7): A6:=RowOperation(A5,[1,4],7*P1): A7:=RowOperation(A6,[2,4],10*P2): A8:=RowOperation(A7,[3,4],5*P3): A9:=RowOperation(A8,[5,4],-10): A10:=RowOperation(A9,[6,4],-5): A11:=RowOperation(A10,[7,4],-100);

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# Priority 1 finished. Move to Priority 2 (Column 3, Row 5 (tie)) evalf([(20/7)/(10/7), (45/7)/(5/7), (200/7)/(100/7)]);

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# A12:=RowOperation(A11,5,7/10): A13:=RowOperation(A12,[2,5],(10/7)*P2): A14:=RowOperation(A13,[3,5],(5/7)*P3): A15:=RowOperation(A14,[4,5],1/7): A16:=RowOperation(A15,[6,5],-5/7): A17:=RowOperation(A16,[7,5],-100/7);

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# Priority 2 finished. Move to Priority 3, Pivot in Column 2 (last row) # A18:=RowOperation(A17,7,1/10): A19:=RowOperation(A18,[3,7],(3/2)*P3 ): A20:=RowOperation(A19,[4,7],-1/2): A21:=RowOperation(A20,[5,7],-1/2): A22:=RowOperation(A21,[6,7],-3/2);

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# Done... TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2ODg0NTg0NDQ4NjMyMjIyWCwlKWFueXRoaW5nRzYiRiVbZ2whIiUhISEjYW8iKCIrIiIhRiZGJiIiKCIjNSIiJiIkKyJGJkYmRiYiIiRGKSIiJSIjZ0YmRiZGJiEiIkYmRiZGJkYmRiZGJkYmRi5GJkYmRiZGJkYmRiZGJkYuRiYlI1AxR0YmRiYiIiJGJkYmRiZGJiUjUDJHRiZGJkYwRiZGJkYmRiYlI1AzR0YmRiZGMEYmRiZGJkYmRiZGJkYmRjBGJkYmRiYiI1NGLSIjTiIkKydGJQ==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