Consider the problem of assigning three different sizes of airplanes to four routes.
The following table gives the maximum capacity (in the number of passengers) and the number of aircraft available for each type, the number of daily trips that each aircraft available for each type, the number of daily trips each aircraft can make on a given route, and the number of daily trips each aircraft can make on a given route. Can make on a given route and the daily number of customers expected for each route.
route.

The associated operating costs per trip on the different routes, together with the penalty cost (lost profit), for not serving a customer, are summarized below.
summarized below:

Formulate the problem as a linear programming model, to determine the assignment of aircraft to routes that will minimize the total cost of the system
 
 

Passenge r Number of Aircraft daily trips type passenger aircraft II IV A 50 3 2 1 30 8 4 3 3 1 20 10 5 4 2 Daily number of passengers 100 200 90 120