Introduction 



Most formal explanations and many computer programs for solving 

 linear programming problems follow the simplex "tableau" method. As 

 desirable as this method is for enabling the beginning student to see the 

 "whys" and "hows" of linear programming, it is rather complicated. If 

 followed in writing an L. P. problem solving program where the origin 

 (zero production) is not feasible, this method unnecessarily uses up a 

 sometimes short supply of computer storage space and is vulnerable 

 to a computer "bug" resulting from an inadequate value "M" for the 

 slack variable (s) . 



This bulletin describes a technique (or algorithm) for solving L. P. 

 problems that is based on rules derived by simple high school algebra 

 rather than the intuitive descriptive approach or the more formal math- 

 ematical approach. It draws on the simple mathematical characteristics 

 of the derived rules to determine the logical sequences of the problem 

 solution and also to eliminate the need for artificial variables and high 

 negative "M" values in problems where zero production is not allowed. 



The technique is such that, for a clearer understanding, the ex- 

 planation will begin with the set-up of a simple problem and proceed 

 rapidly to the rules of the technique (the algorithm). It is important 

 to point out that the rules presented herein are specifically oriented to 

 the method presented for setting up the problem constraints. 



The precise point of departure of this technique from those pre- 

 sented by others (Baumol [1], Heady and Candler [2], Stiefel [3], 

 Vajda [4, 5] for example) is the placing of the equal sign when the 

 inequality constraints are changed into equalities.^ This modification in 

 turn leads to a unique method of handling "greater-than-or-equal-to" 

 constraints that does not require the use of artificial variables and the 

 corresponding high negative values. 



IS; = EXi ± Ci rather than ZXj ± S; = Ci 



1 



