more-simplex-examples

# more-simplex-examples - obj r1 r2 r3 Profit 1 0 0 0 X1 X2-2...

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Profit X1 X2 X3 S1 S2 S3 RHS ratio obj 1 -2 -3 1 0 0 0 0 r1 0 1 2 2 1 0 0 6 3 r2 0 3 -1 1 0 1 0 9 negative r3 0 2 3 5 0 0 1 20 6.6666667 Convert the pivot element to 1 by dividing every element in that row by 2 r1-b 0 0.5 1 1 0.5 0 0 3 Use multiples of r1-b to elminate the non-zero entries in the pivot column. To zero out the -3, add 3xr1-b to the Obj obj 1 -2 -3 1 0 0 0 0 r1-bx3 0 1.5 3 3 1.5 0 0 9 obj-b 1 -0.5 0 4 1.5 0 0 9 To zero out the -1 add r1-b to r2. r2 0 3 -1 1 0 1 0 9 r1-b 0 0.5 1 1 0.5 0 0 3 r2-b 0 3.5 0 2 0.5 1 0 12 To zero out the 3 subtract 3xr1-b from r3 (or add -3xr1b) r3 0 2 3 5 0 0 1 20 r1-bx(-3) -0 -1.5 -3 -3 -1.5 -0 -0 -9 r3-b 0 0.5 0 2 -1.5 0 1 11 Assemble the new matrix Profit X1 X2 X3 S1 S2 S3 RHS Obj-b 1 -0.5 0 4 1.5 0 0 9 r1-b 0 0.5 1 1 0.5 0 0 3 6 r2-b 0 3.5 0 2 0.5 1 0 12 3.4285714 r3-b 0 0.5 0 2 -1.5 0 1 11 22 There is a negative number in the obj, so repeat the pivot Profit X1 X2 X3 S1 S2 S3 RHS obj-c 1 0 0 4.28571429 1.5714286 0.1428571 0 10.714286 r1-c 0 0 1 0.71428571 0.4285714 -0.142857 0 1.2857143 r2-c 0 1 0 0.57142857 0.1428571 0.2857143 0 3.4285714 r3-c 0 0 0 1.71428571 -1.571429 -0.142857 1 9.2857143 No negative elements on Obj so we are done. Profit 10.714286 X1 3.4285714 red cost X3 4.2857143 X2 1.2857143 sh price r1 1.5714286 X3 0 sh price r2 0.1428571 S1 0 sh price r3 0 S2 0 S3 9.2857143

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X1 X2 X3 RHS Used Slack S.P obj 2 3 -1 0 10.7142857 r1 1 2 2 Le 6 6 0 1.5714286 y1 = 1.57 r2
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