A manufacturing firm produces two products A and B. Each of these products must be processed through two different machines. However, both the machines are also used to produce other products. Thus, the available machine hours for the production of A and B per week are 12 hours on machine 1 and 8 hours on machine 2. Each unit of product A requires 2 hours of time on both machines. On the other hand, each unit of product B requires 3 hours of time on machine1 and 1 hour on machine 2. The profit per unit of product A and B are RM 6 and RM 7 respectively. The firm can sell as many units of each product as it can manufacture. Formulate the objective function and the constraints.