A manufacturing company produces two products: Product A and Product B. The company has a limited amount of resources, and it wants to maximize its daily profit. The profit per unit of Product A is $20, and the profit per unit of Product B is $25. Each unit of Product A requires 3 hours of labor and 2 hours of machine time, while each unit of Product B requires 2 hours of labor and 3 hours of machine time. The company has 240 hours of labor and 180 hours of machine time available each day.

a) Formulate the linear programming model to maximize the daily profit for the company.

b) Use graphical method to solve the model and find the optimal production plan for the company.

c) What is the maximum daily profit the company can achieve with the optimal production plan?