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addition of automobiles additional automobiles amount of purpose automobile allocation decisions automobile availability constraints automobile ownership decisions automobile trip Brown University dual problem dual variables essential trip purposes Golob household automobile allocation household automobile availability household requires implicit costs implicit value integer linear program integer program interdependence of household level of purpose members with respect mode choice model formulation model of household model presented models of automobile Motors Corporation notice of trip number of automobiles number of household objective function opportunity cost optimality conditions optimization model period programming formulation public transportation purpose p required round trip travel satisfy essential purposes satisfy purpose satisfying essential trip savings resulting stock of automobiles THEORY OF HOUSEHOLD tikT total number transit trip Transportation and Urban travel behavior travel demand decisions trip costs trip frequencies trip purpose satisfaction unit of purpose Urban Analysis Department value of additional XikT