Summary of Rules for Determining Pivot 

 Rows and Pivot Columns and the 

 Pivoting Operation 



Once the constraints for an L. P. problem are set up in inequality 

 form, they are made into equalities by adding or subtracting slack vari- 

 ables. These equality constraints are then restated in terms of the posi- 

 tive slack variable, and set up in the following matrix form: 



X2 



KPo) 



Si = 



82 = 



To the bottom row of this matrix, the objective function is added. If the 

 objective function is to be maximized, it takes the form: Z =r X^ -|- X2 

 . . . X„ . If it is to be minimized, it takes the form: — Z ^ — Xj 

 — X2 — ... — X n . The objective solution is initially zero. 



I. If any negative figures appear in the last column: 



Rules for Removing Negative Resources 



Neg-1. The row in which the negative figure appears is the pivot 

 row. 



Neg-2. The pivot element must be positive. 



Neg-3. The pivot column is arbitrarily chosen. 



Neg-4. If there are two or more negative numbers in the- last col- 

 umn, then, using the arbitrarily chosen pivot column, Q- 

 values are generated for each row containing a negative 

 number. The row with the largest absolute value of Q will 

 be the pivot row (all Q's will be negative since the poten- 

 tial pivot element must be positive and since only the nega- 

 tive last row numbers are of concern). 



II. Once the pivot row and pivot column are determined, the pivoting 

 process develops a new matrix by: 



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