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July 6th, 2017, 09:46 AM  #1 
Newbie Joined: Jun 2017 From: Wisconsin Posts: 15 Thanks: 0  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. 
July 6th, 2017, 11:27 AM  #2 
Senior Member Joined: Jun 2015 From: England Posts: 821 Thanks: 243 
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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basic, explain, method, simplex, variables 
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