subject to
In order for the above problem to be feasible, it is of course necessary that the total demand for park&ride trips does not exceed the total amount of parking space available at the parking lots, i.e.
The less slack there is in the above inequality, the harder the problem will become to solve. To avoid problems of degeneracy we also assume that 
0 for all 
.
By introducing the dual variables 
for the constraints (5) and 
for constraints (6) and applying again the Kuhn-Tucker optimality conditions, we obtain a model of the following functional form:
subject to (5) and (6).
From this, we can obtain the dual problem formulation as follows:
