A car rental agency has a budget of $2.85 million to purchase at most 120 new cars. The agency will purchase either subcompact cars at $19,000 each or midsized cars at $38,000 each. From past rental patterns, the agency decides to purchase at most 50 midsized cars and expects an annual profit of $7,500 per subcompact car and $13,000 per midsized car. How many of each type of car should be purchased to obtain the maximum profit while satisfying budgetary and other planning constraints?