Professor Yataha needs to schedule six round-trips between Boston and Washington, D.C. 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 exceeds 5. US Air gives 1500 miles per ticket plus 10,000 extra for each 6 tickets. Continental gives 1800 miles per ticket plus 7000 extra for each 5 tickets. Professor Yataha wishes to allocate the 12 one-way tickets among the three airlines to maximize the total number of bonus miles earned.