The analyst can solve for optimal usage by forming the Lagrangian and applying the Kuhn-Tucker conditions. Designating vehicle type 1 as a vehicle type to which the household allocates some non-zero amount of usage (note that the household should use at least one of the Kvehicle types, given that the household will travel during the year), and using algebraic manipulations, the Kuhn-Tucker conditions may be written as (see, Bhat, 2008):
by forming the Lagrangian and applying the Kuhn-Tucker conditions. Designating vehicle type 1 as a vehicle type to which the household allocates some non-zero amount of usage (note that the household should use at least one of the K 
, (3)