Replies to post #139 on The Weekend Lounge

[Soapy Bubbles]

Yes. 2 is the pivot and you use row ops to get it to 0 since you want (usually) to eliminate it.

[Soapy Bubbles]

Basically you're looking to make the xyz matrix diagonal like / or \ as to make finding the values for x, y, and z simpler. If possible, isolate y and z using row ops and then work backwards to x. (Usually you isolate n-1 vars and backsolve the last one.)

You know the max is 28 by the tabu.

[Soapy Bubbles]

 
 Tableau #3 
 x      y      z      s1     s2     r              
 1      0      1      1/5    2/5    0      13      
 0      1      0      -2/5   1/5    0      2       
 1      0      0      0      1      1      28   
 

RREF has to get you to this. When you read the first two lines (the important ones since r=0), you know:

x+z=13
y=2 <-- Isolated for you.

but then you have the last row (r=1) which is the maximized result. So use z-13=x and y=2 in R=28. Get the z. Now get the x. You're done.

[Soapy Bubbles]

Oh, one thing of advice (forgot it until now).

The last tabu ONLY WANTS R=1 IN ONE ROW.

Else you need to keep reducing or messed up.

[Soapy Bubbles]

http://www-fp.mcs.anl.gov/otc/Guide/CaseStudies/simplex/feasible.html

Worth printing out someday -- good example site.

[Soapy Bubbles]

And the guiding rule is to make the xyz matrix DIAGONAL w/ as few off diagonal elements as possible. If you do that, you can isolate the variables w/ a little hassle. If you're allowed to use a HP or TI, they do RREF.