3- LP Formulation and Lingo Model (25 points) The airline company has 2 types of aircrafts, and it has to assign route requires certain number of trips. The aircrafts has 3 routes. Every required number of trips and the cost associated for each trip depending on the aircraft type is given. The number of passengers for each route is known. If a passenger is not served (passenger cannot fly because of the company), company must pay a penalty cost for each lost customer Following data is given for the aircraft problem. Aircraft Capacity Number of daily trips on route (passengers) Number of aircraft 2 3 10 16 Daily number of customers 1000 2000 type 1 2 100 60 1 3 4 2 3 2 3 800 The associated costs including the penalty cost for lost customers are: Operating cost (5) per trip on route Aircraft type 1 2 3 100 110 80 90 100 Penalty (S) per lost customer 8 9 120 10 a) (10 points) Define LP model for the above problem. (4 pts) Define the decision variables. (2 pts) Write down the LP objective function. (4 pts) Write down the LP constraints. b) (10 points) Define LINGO scripts for (3 pts) SET definition and DATA file (2 pts) Objective function by using loop functions (5 pts) Constraints by using loop functions c) (5 points) Find the results with LINGO for the problem and interpret the solution (explain the optimum solution)