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July 6th, 2017, 09:46 AM   #1
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Can someone explain Basic Variables in the Simplex Method?

I'm very confused by Basic variables in the simplex. They seem to be important so I want to have a good grasp of them. Here is an example from my textbook. Simple Tableau table:

x1 x2 x3 s1 s2 z
1 1 1 1 0 0 100
10 4 7 0 0 0 500
______________________
-120 -40 -60 0 0 1 0

It says the following:

- To get a feasible solution all variables must be non negative (are they talking about the constraints? Because z variables are negative)
- To get a unique feasible solution set 3 of the 5 variables equal to 0 (Which 3 do we set to 0 and why?)
- If there are m equations then m variables can be non zero(So if we have 3 equations, then 3 variables can be non zero? Once again how do we choose which variables are non zero?)
- These m nonzero variables are called basic variables

So in this example they set x1 = 0, x2 = 0, x3 = 0 then s1 =100, s2 = 500(basic variables). Confused as to why they set x1, x2 and x3 to 0.
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July 6th, 2017, 11:27 AM   #2
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A system of m equations in n unknowns with m<= n is in canonical form with a distingusihed set of m basic variables if each basic variable has a coefficient of 1 in one of the equations and zero in all the others and further that each equation has exactly one basic variable (with a coefficient of 1).

The equation set must be algebraically manipulated to this format for the Simplex method to operate.
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