 My Math Forum Can someone explain Basic Variables in the Simplex Method?

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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: 915 Thanks: 271 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. Tags basic, explain, method, simplex, variables Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post pass92 Linear Algebra 2 November 2nd, 2016 02:20 PM texaslonghorn15 Linear Algebra 1 June 10th, 2013 01:13 PM Timk Linear Algebra 0 April 24th, 2012 09:19 AM adel87 Applied Math 0 March 23rd, 2010 12:38 PM mibuon Algebra 0 March 7th, 2010 11:52 PM

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