Transcription of Chapter 6Linear Programming: The Simplex Method
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Chapter 6Linear Programming: The Simplex Method
Chapter 6 Linear programming : TheSimplex MethodWe will now consider LP (Linear programming ) problems that involvemore than 2 decision variables. We will learn an algorithm called thesimplex Method which will allow us to solve these kind of Problem in Standard FormWe start with defining the standard form of a linear programmingproblem which will make further discussion linear programming problem is said to be astandard max-imization problem in standard formif its mathematicalmodel is of the following form:MaximizeP=c1x1+c2x2+..+cnxnsubject toa11x1+a12x2+..+a1nxn b1 am1x1+am2x2+..+amnxn bmx1, x2, .. , xn 0wherex1, x2, .. , xnaredecisionvariables,c1, .. , cn,a11, .. , amnare any real numbers, andb1, .. , bm 0 arenonnegative real :Any linear programming problem (in the form we definedearlier) can be converted intothe standard maximization problemin standard 6.
The simplex method de nes an e cient algorithm of nding this speci c solution of the system of linear equations. Therefore, we need to start with converting given LP problem into a system of linear equations. First, we convert problem constraints into equations with the …
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