# Example 3: Preemptive programming
with(LinearAlgebra):
interface(rtablesize=11);
# Vars: x1 x2 s1p s2p s3p s1m s2m s3m (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>>;
#
A2:=RowOperation(A,[1,4],-P1):
A3:=RowOperation(A2,[2,5],-P2):
A4:=RowOperation(A3,[3,6],-P3);
# Work through Priority 1 first (Row 1): Pivot in Column 1
evalf([40/7,60/10,35/5,600/100]);
#
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);
# 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)]);
#
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);
# 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);
# Done...