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# Simplex Tableau Multiple Solutions or Single Solution? watch

1. Ok, so when I get to the final tableau, I know how to tell if the LP is unbounded (all ratios are negative and you still have a negative/positive (max/min) value in your objective function.

But how can you tell if your final tableau shows the LP has multiple solutions, or a single solution?

For example:

Where the top columns are: z, x1, x2, s1, s2, s3, Val
and the rows are: s1, x2, x1, z

Where z is the objective function, s1,s2,s3 are slack variables. Apparently this problem has multiple solutions, but why not just x2=1 and x1=4? What is the general way of working it out and finding the multiple solutions?

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2. anyone?
3. (Original post by 3thr3e)
anyone?
I'm not overly familiar with it, but looking through Wagner's Principles of Operations Research, he says:

"This condition (viz. multiple solutions) is indicated by a zero coefficient for two or more nonbasic variables in the final Row 0."
4. (Original post by ghostwalker)
I'm not overly familiar with it, but looking through Wagner's Principles of Operations Research, he says:

"This condition (viz. multiple solutions) is indicated by a zero coefficient for two or more nonbasic variables in the final Row 0."
Thanks, this makes sense. But has anyone got any idea on how to then represent the solutions?
5. (Original post by 3thr3e)
Thanks, this makes sense. But has anyone got any idea on how to then represent the solutions?
Again from Wagner, you'd need to find all basic optimal solutions, and then the set of solutions is any postive-weighted average of all of these.

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