The AU Auto Company is a highly respected auto manufacturing firm which is famous for providing fully customized car models. The company has received an order for two different type of cars, Model A and B. The only capacity problem the company is facing is the labor time. Manufacturing one Model A car requires 3 weeks and manufacturing one Model B car requires 2 weeks. The company has a time window for 12 weeks to manufacture a product mix of Model A and B cars. Model A is the signature product of the company; therefore, the company wants that of all cars manufactured, at least 25% should be Model A. However, since its price is very high, the company knows that they cannot sell more than 3 cars. The company can sell Model A for $8mil and Model B for $5mil. What should be the product mix in order to maximize the total income? Use graph method to solve this problem.