Simultaneous equation and variable scaling

Reductions in numerical disparity across the coefficients are made when equations and variables are simultaneously scaled.  If I scale all variables multiplying coefficients by SCj , all rows dividing coefficients by SRi and the objective dividing coefficients by SO then I get the following table from McCarl and Spreen applies.  In the resultant problem the coefficients after scaling are given by the formulae

and the relationships between solution items before and after scaling is given by

Fortunately, GAMS and the GAMS solvers do this for us adjusting all solutions so they look as if they were never scaled. But this table does show the solutions are equivalent only differing by multiples of the scaling factors.

Example of scaling