When the primal is a normal min problem with m constraints and n variables, then the dual problem will be normal max problem with m variables and n constraints. Thus, it can be written as follows.
The shadow price of the constraint is amount by which the optimal z-value is improved if we increase by 1.
Thus, the optimal z-value is. Suppose, we want to increase any one of the value such that the difference from the corresponding new b value is. So,
Now, equation (1) – equation (2) implies
Thus, in general it can be concluded that for any increase in, the