East Coast Airlines operates a hub at the Halifax International Airport. During the summer, the airline schedules seven flights daily from Halifax to Toronto and 10 flights daily from Toronto to Halifax according to the following schedule.

The flight crews live in Halifax or Toronto, and each day a new crew must fly one flight from Halifax to Toronto and one flight from Toronto to Halifax. A crew must return to its home city at the end of each day. For example, if a crew originates in Toronto and flies a flight to Halifax, it must then be scheduled for a return flight from Halifax back to Toronto. A crew must have at least one hour between flights at the city where it arrives. Some scheduling combinations are not possible; for example, a crew on flight 1 from Halifax cannot return on flights A, B, or C from Toronto. It is also possible for a flight to ferry one additional crew to a city in order to fly a return flight, if there are not enough crews in that city.
The airline wants to schedule its crews 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 work day, is bad for crew morale, and is expensive for the airline. Formulate a linear programming model to determine a flight schedule for the airline and solve using Excel. How many crews need to be based in each city? How much ground time will each crew experience?

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Arrive Leave Arrive Leave Halifax Flight Toronto Toronto Flight Halifax 9 A.M. 6 A.M. 9 A.M. 6 A.M. 7 A.M. 10 A.M. 11 A.M. B 8 A.M. 11 A.M. 8 A.M. Noon 9 A.M. 3 1 P.M. 10 A.M. 6 P.M. D 3 P.M. 3 P.M. Noon 8 P.M. 5 P.M. 5 5 P.M. 2 P.M. 7 P.M. 10 P.M. 6 P.M. 3 P.M. 11 P.M. G 8 P.M. 7 9 P.M. 6 P.M. Н 7 P.M. 10 P.M. Midnight 9 P.M.