Delta American Airlines (DAA) needs to replace some of the aircraft in its aging fleet. It has the choice of three different models, with the characteristics shown below.
DAA currently can accommodate 20,000 hours per year of maintenance; however, by spending $3 million, this capacity can be raised to 25,000 hours per year. The needs of the airline are such that at least 12 model 1 planes, or 10 model 2 planes, or 15 model 3 planes must be purchased. Given that DAA can invest at most $100 million (including any expansion of maintenance facilities), how many planes of each type should it purchase to maximize yearly profits? Formulate this situation as an optimization problem.