LP10. (Airline Scheduling Problem, based on (TY08]) A small airline would like to find an optimal schedule of flights to maximize profit. The airline operates flights on 3 lines between 4 cities: Cincinatti-Roanoke, Atlanta- Roanoke and New York-Roanoke. The table below shows the distances (in nautical miles), daily demands and market-clearing fares (in dollars) per seat for each of these lines: distance demand (to) demand (fro) fare per seat New York-Roanoke 375 480 670 270 Atlanta-Roanoke 520 630 230 Cincinatti-Roanoke 220 430 380 180 The airline has decided to purchase two types of aircraft to satisfy its needs: Embraer 145 and Avro RJ-100. The characteristics of each machine are given in the table below: Aircraft EMB-145 Avro RJ-100 number of seats 50 100 block speed (knots) 400 425 operating cost per hour of usage $1850 $3800 maximum utilization per day 13 hrs. 12 hrs. (a) Solve the integer programming problem of maximizing the profit using the following sets of decision vari- ables: numbers of aircrafts of each type in the fleet and numbers of flights between each pair of destinations (separately in each direction) using aircraft of each type. Take into account the aircraft availability and demand fufillment constraints. In particular, take into account that the number of flights between each pair of destinations should be the same in both directions. (b) Do the same as in point (a) subject to an additional constraint that the minimum number of flights (in each direction between Atlanta and Raonoke should be 10. LP10. (Airline Scheduling Problem, based on (TY08]) A small airline would like to find an optimal schedule of flights to maximize profit. The airline operates flights on 3 lines between 4 cities: Cincinatti-Roanoke, Atlanta- Roanoke and New York-Roanoke. The table below shows the distances (in nautical miles), daily demands and market-clearing fares (in dollars) per seat for each of these lines: distance demand (to) demand (fro) fare per seat New York-Roanoke 375 480 670 270 Atlanta-Roanoke 520 630 230 Cincinatti-Roanoke 220 430 380 180 The airline has decided to purchase two types of aircraft to satisfy its needs: Embraer 145 and Avro RJ-100. The characteristics of each machine are given in the table below: Aircraft EMB-145 Avro RJ-100 number of seats 50 100 block speed (knots) 400 425 operating cost per hour of usage $1850 $3800 maximum utilization per day 13 hrs. 12 hrs. (a) Solve the integer programming problem of maximizing the profit using the following sets of decision vari- ables: numbers of aircrafts of each type in the fleet and numbers of flights between each pair of destinations (separately in each direction) using aircraft of each type. Take into account the aircraft availability and demand fufillment constraints. In particular, take into account that the number of flights between each pair of destinations should be the same in both directions. (b) Do the same as in point (a) subject to an additional constraint that the minimum number of flights (in each direction between Atlanta and Raonoke should be 10