


A STANDARD MAXIMIZING PROBLEM is a linear programming
problem which satisfies all of the following 4 CONDITIONS (Rolf, pg.263) : 



Reference : An example of how to apply the following procedure to a nonstandard problem is available, with abundant comments and crossreferences.
Reference : Many EXERCIZES are available for each step of this method.




Convert all constraints to equations with slack variables, and then write the problem as a tableau with some negative right sides, with or without a ZCOLUMN. 


FINDING THE PIVOT
(steps

Locate the row containing the most negative righthand number. This row will be called the INDICATOR ROW. If no righthand number is negative, then your tableau is STANDARD. 

INDICTORS will consist of all numbers in the row found in NS3, except the rightmost number; the PIVOT COLUMN will contain the most negative of these indicators. If no indicator is negative, then there is no pivot column, and the problem is unsolvable. 

Form RATIOS or QUOTIENTS for all (nonobjective) rows : for each row, divide the rightmost number by the number in the pivot column. 

The PIVOT will be in the ROW with smallest nonnegative ratio. Note that 0(+1) and 0(1) are both numerically zero, but in calculating RATIOS, consider 0(+1) as positive (OK), and 0(1) as negative (not OK). 

Perform a pivot transformation on the above pivot (Rolf, Pg 98). Check out the PIVOT ENGINE to speed pactice. 

If all rightmost (nonobjective row) entries are nonnegative, then phase I is ended. PHASE II now consists of applying steps 39 of the standard maximizing procedure to the new tableau obtained in step NS7 above. Note: PHASE II is described as step #7 on Page 329 of our text, Rolf. 

Otherwise, if some rightmost (nonobjective row) entry is negative, apply steps NS3 through NS9 to the new tableau obtained in NS7. 