Suppose I have the problem below
To solve this problem I would not ordinarily use scaling, but the problem provides a vehicle to illustrate scaling procedures and consequences. The biggest numbers in the problem within the constraint matrix are in the first third and fourth constraint equations. Thus, suppose I convert the units of the first constraint by dividing all coefficients by 10000 and since it appears X1 is in the same units convert the units of X1 to 10000's of items by multiplying all coefficients under it by 10000. Simultaneously, I will divide all coefficients in the third constraint equation by 1000 and in the fourth by 50. The resultant model is
Now suppose I divide all coefficients in the X4 column by 50 and all coefficients in the objective function by 10000. The final scaled problem then becomes
The disparity in numbers is now much less and this is what I try to achieve in scaling. Furthermore when I solve the problem now in numerically simpler form I can reconstruct the solution to the original problem by simply multiplying and dividing solution items by the scaling factors using the above table.