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Chapter 6Linear Programming: The Simplex Method

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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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