with(LinearAlgebra): This is Example 4 from class (Exercise 3 in the textbook) using TVs and VCRs. The default size of an array shown to the screen will be 10 columns, so the next command changes that for our big matrix! interface(rtablesize=11);

IiM2

A:=<<0,0,0,300,150,3>|<0,0,0,200,100,2>|<0,0,0,1,0,0>|<P1,0,0,-1,0,0>|<0,P2,0,0,1,0>|<0,0,0,0,-1,0>|<0,0,0,0,0,1>|<0,0,P3,0,0,-1>|<0,0,0,20000,11000,200>>;

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

#Clear P2 to get a BFS A1:=RowOperation(A,[2,5],-P2);

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

Pivot in Column 1, Row 4 (from ratio test below). evalf([(20000/300), 11000/150, 200/3]);

NyUkIitubW1tbSEiKSQiK0xMTEx0RiVGIw==

A2:=RowOperation(A1,4,1/300): A3:=RowOperation(A2,[2,4],150*P2): A4:=RowOperation(A3,[5,4],-150): A5:=RowOperation(A4,[6,4],-3);

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

Therefore, this tableau is "optimal" with basic variables x1, s2m, s3p. x_1= 66.66, x_2=0, s_1=0, s_2^-=1000 (we did not meet our profit goal), and s_3=0