In linear programming problems the shadow price of a constraint is the difference between the optimised value of the objective function and the value of the objective function, evaluated at the optional basis, when the right hand side (RHS) of a constraint is increased by one unit.
Suppose i get a shadow price S[i] , corresponding to the i-th constraint. If decrease the value of the resource by one unit, do i get a decrement of the objective function equal to the shadow price itself ? If yes, what is the reason for this symmetry of Shadow Price ?