Optimization shadow price

The multiplier tells how the optimal value of the objective func tion changes for this small change in the value of a constraint while holding all the other constraints at zero. It is for this reason that they are often called shadow prices. 

The Lagrange multipliers in a constrained nonlinear optimization problem have a similar interpretation to the dual variables or shadow prices in linear programming. To provide such an interpretation, we will consider problem (3.3) with only equality constraints that is,... 

The following Eqs. (10) and (11) give the changes of the variables in the basis and profit for changes Afo,. Referring to Eq. (11), the units on the Lagrange multiplier are dollars per unit mass or volume, hence the name shadow prices. For the optimal solution to... 

Second Law quantities such as available-energy and negentropy need not be introduced explicitly into the optimization although their effects are evaluated (indirectly) by the shadow and marginal prices. Furthermore, any required Second Law based prices can be obtained by using Equations 17 and 18 or by way of a thermoeconomic accounting technique (5,15). 

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