Please formulate an integer programming model that can be used to solve the following problem. Clearly state your decision variables, objective, and constraints. Kindly note that you do NOT need to implement this problem in Excel. Please follow the instructions given in the problem/satisfy all requirements.You need to schedule six round-trips between Pittsburgh and Boston for candidates that will interview for internship positions in your company. The route is served by three airlines: Eastern, US Air, and Continental and there is no penalty for the purchase of one-way tickets. Each airline offers bonus miles for frequent fliers. Eastern gives 1000 miles per (one-way) ticket, plus 5000 extra miles if the number of tickets in a month reaches 2, and another 5000 miles if the number reaches 6. US Air gives 1500 miles per ticket, plus 10,000 extra for every 6 tickets. Continental gives 1800 miles, plus 7000 extra for every 5 tickets. What is the best way to allocate the 12 one-way tickets among the three airlines to maximize the total number of bonus miles earned? Formulate an integer programming model for this problem (clearly state your decision vari- ables, objective, and constraints). You do not need to implement your model in Excel.