Potential Pivot Element. For reasons explained in Appendix B, 

 any potential pivot element must he negative and the resource value in 

 any potential pivot roiv m-ust be positive; therefore, all the Q-values 

 that are of concern will be negative.^ 



The pivot column contains the largest bottom positive element and a po- 

 tential pivot element (negative). 

 The pivot row generates the smallest absolute value of Q. 



Figure 1 : Beginning matrix of example problem. 



Rules for the Pivoting Procedure 



The rules for the pivoting procedure, which are derived in Appen- 

 dix B, are as follows: 



A new matrix is developed by: 



Pivoting Rules 



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

 value. 



PR-2. Changing the other values in the pivot column 

 by dividing each by the old pivot element. 



PR-3. Changing the other values in the pivot row by 

 dividing each by the old pivot element and 

 giving it the opposite sign. 



PR-4. Changing all other elements in the matrix by 

 subtracting from each: the value obtained by 

 multiplying the element in the same column 

 and pivot row by the element in the same row 

 and pivot column, then dividing this product by 

 the pivot element. ("Rectangle Rule") 



1 At this point, we are not concerned with situations in which negative Q- 

 values cannot be generated. This will be covered later, see bottom of page 12. 



