Alpha Airline wishes to schedule no more than one flight out of a given airport to each of the following cities: C, D, L, and N. The available departure slots are 8 A.M., 10 A.M., and 12 NOON. Alpha leases the airplanes at the cost of $5000 before and including 10 A.M. and $3000 after 10 A.M., and is able to lease at most two per departure slot. Also, if a flight leaves for location N in a time slot, there must be a flight leaving for location L in the same time slot. The expected profit (in $1000) contribution before rental costs per flight is shown in the table below. Formulate a model for a profit-maximizing (after deducting rental cost) schedule. Define your decision variables carefully; write the objective function and all relevant constraints.

Time Slot	8 A.M.	10 A.M.	12 Noon
C	10	6	6
D	9	10	9
L	14	11	10
N	18	15	10