Pivoting Rules 

 PR-1. Changing the old pivot element to its reciprocal value. 



PR-2. Changing all other elements in the pivot column by divid- 

 ing them by the old pivot element. 



PR-3. Changing all other elements in the pivot row by dividing 

 them by the old pivol element and giving them the oppo- 

 site sign. 



PR-4. Changing all other elements by subtracting from them the 

 value derived from the "rectangle rule" (see PR-4, page 4) . 



This process of determining the pivot row and column and pivoting 

 matrix is 

 last column. 



the matrix is continued until all negative values are eliminated from the 



III. When this is accomplished, or when the initial matrix does not 

 contain negative values in the last column, and when positive values are 

 contained in the bottom row (excepting the solution box), the pivot 

 row and column for successive pivoting processes are determined as 

 follows : 



Rules for Determining Pivot Columns and Pivot Rows 



Pivot Column: The column with the largest positive bottom element 

 and which contains a negative potential pivot element 

 becomes the pivot column. 



Pivot Row: Q-values are generated for all rows where the potential 

 pivot element is negative. The smallest absolute value of Q 

 determines the pivot row (it is obvious that again all 

 values of Q will be negative) . 



Once the pivot row and column have been determined, the pivoting 

 process continues as previously described (see II, page 10). 



This method (III) of determining the pivot row and column, and 

 the pivoting process (II) are continued until only negative values are 

 contained in the bottom row. The problem is then solved. 



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