subject to 
, 
.
The Kuhn-Tucker optimality conditions of the dual problem can be written as follows:
The optimal values of the dual variables associated with the parking capacity constraints, 
, are the shadow prices associated with the ``last'' parking space on parking lot k. They correspond to the additional impedance (or weighted cost) which would need to be imposed at the parking lot in order to defer enough potential trips to other parking lots to meet the given capacity 
. For parking lots which do not reach capacity ( 
) this cost is obviously zero. For a parking lot which is capacity bound, 
can be used as an indicator of the cost imposed to the system by limiting its capacity to .
Solution Algorithm
As the dual problem (9) does not have any
