# Simplex question

Discussion in 'Mathematics' started by Piranha, Feb 2, 2012.

1. ### PiranhaStar commenter

Thanks for the thought, lizziec. I can see what you mean, but I am not convinced it is right. Given enough time, I could try a few examples with both methods, but still wouldn't be sure it always worked.
I don't like not being able to explain something. I only feel comfortable teaching a technique if I think I can explain why we do it this way.

2. ### Anna-Luise

I'm not an OR expert. I've never even taught D1. I am interested in your question though. I've looked into it a little. If there are only two variables in the problem and they're linked by an equation then you must be right that one can be eliminated but this makes the problem trivial. Could you give an example or two of the the sort of problem you're thinking about, please?

3. ### florapost

i know even less than anna-luis, but surely if the slack variable is zero, then you do have x+y=1?

4. ### drnfp

Could you give the whole question, or a reference to the book? I'm assuming that the book is referring to questions in more than 2d?
Cheers

5. ### drnfp

For a constraint like
x+y=1
You introduce what's called an artificial variable, say a1, so that
x+y+a1=1
Suppose the original objectice function was z = 3x+4y, this is then modified to
z=3x+4y-Ma1, where M is an arbitrarily large number. When the Simplex tableau starts, it
assumes the original variables are all zero, hence a1=1 and so the method can start.
Without a1, you would have 0=1. The M introduced into z then forces a1 out of the solution, so
a1=0 and the contstraint is satisfied. So the use of a1 is just to give the method a starting
point.

As to whether you can use any equality constraints to eliminate a variable, the answer is yes.
The reason it's not done is purely the mess involved in rewriting all the constraints.
Remember, in ''real life'' problems there could be a lot of variables and more than one equality
constraint. The above method actually involves less computation.

I hope this helps.

6. ### drnfp

Sorry about the typesetting, it didn't look like that when I did it?!