A manufacturing firm must decide how to allocate next week's time on an injection machine, which produces two types of products A and B. These two products can be produced on the machine at different rates: 200 tons of A can be produced in 1 hour when only A is produced, and 140 tons of B can be produced in 1 hour when only B is produced. They also yield different profits: Each ton of product A brings in $25, and each ton of product B brings in $30 profit. Based on currently booked orders, the company has decided that product A should be produced at a maximum of 6000 tons and product B should be produced at a maximum of 4000 tons. Given that there are 40 hours of production time available this week, the problem is to decide how many tons of product A and how many tons of product B should be produced to yield the greatest profit. Suppose that the currently booked orders have been changed and the company has decided that product A should be produced at a minimum of 5000 tons and product B should be produced at a minimum of 2000 tons. Formulate and solve the problem using the Big M method.