A toy company produces two types of toy cars, model X and model Y. The company can produce up to 100,000 toy cars per month and has a production cost of $2 for model X and $3 for model Y. The company wants to produce at least 20,000 of model X and 30,000 of model Y. Each model X car sells for $5, while each model Y car sells for $6. Determine the number of each type of toy car the company should produce to maximize its profit.