CASE STUDY 2-(CHS) XA Airlines must staff the daily flights between New York and Chicago shown in Table 81. Each of XA's crews lives in either New York or Chicago. Each day a crew must fly one New York-Chicago and one Chicago-New York flight with at least 1 hour of downtime between flights. XA wants to schedule the crews to minimize the total downtime. Set up an assignment problem that can be used to accomplish this goal. (Hint: Let x = 1 if the crew that flies flight i also flies flight j, and x= 0 otherwise. If x-1, then a cost c; is incurred, corresponding to the downtime associated with a crew flying flight i and flight j). Of course, some assignments are not possible. TABLE 81 Leave Chicago Flight 1 2 3 4 5 6 7 Arrive New York 6 A.M. 9 A.M. 12 noon Flight 1 2 10 A.M. 1 P.M. 4 P.M. 3 P.M. 7 P.M. 4 5 P.M. 9 PM. 5 7 P.M. 11 P.M. 6 8 P.M. 12 midnight 7 AWN 3 Leave New York 7 A.M. 8 A.M. 10 A.M. 12 noon 2 P.M. 4 PM. 6 PM. Arrive Chicage 9 A.M. 10 A.M. 12 noon 2 P.M. 4 PM. 6 PM. 8 P.M. > Formulate a model to find the flight assignments that minimize the total downtime and by using any solver how many crews should be based in each city, assume that at the end of the day, each crew must be in its home city.