A company produces two types of products, Product A and Product B. The company has a limited budget and wants to maximize the total revenue generated from the two products. The revenue per unit of Product A is $50, and the revenue per unit of Product B is $80. Each unit of Product A requires 4 hours of labor and 2 hours of machine time, while each unit of Product B requires 6 hours of labor and 3 hours of machine time. The company has a budget of $20,000 and 600 hours of labor and 300 hours of machine time available.

a) Formulate the linear programming model to maximize the total revenue for the company.

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

c) What is the maximum total revenue the company can achieve with the optimal production plan?