Dragon Airlines operates a hub at the Detroit International Airport. During the summer, the airline schedules 5 flights daily from Detroit to Atlanta and 7 flights daily from Atlanta to Detroit, according to the following schedule:

Flight	Leaving Detroit	Arrive Atlanta
1	6:00	9:00
2	7:00	10:00
3	10:00	13:00
4	16:00	19:00
5	21:00	0:00

Flight	Leaving Atlanta	Arrive Detroit
A	6:00	9:00
B	7:00	10:00
C	10:00	13:00
D	11:00	14:00
E	15:00	18:00
F	19:00	22:00
G	21:00	0:00

The flight crews live in Detroit or Atlanta, and each day a crew must fly one flight from Detroit to Atlanta and one flight from Atlanta to Detroit. A crew must return to its home city at the end of each day. For example, if a crew originates in Atlanta and flies a flight to Detroit, it must then be scheduled for a return flight from Detroit back to Atlanta. A crew must have at least 1 hour between flights at the city where it arrives. Some scheduling combinations are not possible; for example, a crew on flight 1 from Detroit cannot return on flights A or B from Atlanta. It is also possible for a flight to ferry one additional crew to a city in order to fly a return flight. The airline wants to schedule its crews in order to minimize the total amount of crew ground time (i.e., the time the crew is on the ground between flights). Excessive ground time for a crew lengthens its workday, is bad for crew morale and is expensive for the airline. a. Formulate an integer programming model to determine a flight schedule for the airline. Define the decision variables, and formulate the objective function and constraints clearly. b. Suppose that Dragon Airlines relaxed its restriction that each crew must fly one flight from Detroit to Atlanta and one flight from Atlanta to Detroit such that crews can fly two flights in each direction. For instance, a crew can fly Flights 1, D, 4, and G. As before, each crew must return to its home city at the end of each day. Reformulate the problem to minimize the number of crews for Dragon Airlines.