A car rental agency has a budget of $1.8 million to purchase at most 100 new cars. The agency will purchase either subcompact cars at $15,000 each or mid-sized cars at $30,000 each. From past rental patterns, the agency decides to purchase at most 50 mid-sized cars and expects an annual profit of $7500 per subcompact car and $11,000 per mid-sized car. How many of each type of car should be purchased in order to obtain the maximum profit while satisfying budgetary and other planning constraints? Find the maximum profit.