2. The Omega Manufacturing Company produces three different products: products 1, 2, and 3. The number of machine hours required for each unit of the respective product; and available capacity on the machines that might limit output are summarized in the following table: Milling Machine Lathe Grinder Product 1 3 2 2 Product 2 Product 3 week) 1 1 2 1 1 Available capacity (machine hours per 1 60 20 30 The unit profit would be $8, $7, and $6, respectively, on products 1, 2, and 3. The objective is to determine how much of each product Omega should produce to maximize profit. (a) Define the decision variables clearly. (10 pts.) (b) Write the objective function. (10 pts.) (c) Write the constraints (including non-negativity constraints). (10 pts.)

2. The Omega Manufacturing Company produces three different products: products 1,2, and 3. The number of machine hours required for each unit of the respective product; and available capacity on the machines that might limit output are summarized in the following table: The unit profit would be $8,$7, and $6, respectively, on products 1,2 , and 3 . The objective is to determine how much of each product Omega should produce to maximize profit. (a) Define the decision variables clearly. (10 pts.) (b) Write the objective function. (10 pts.) (c) Write the constraints (including non-negativity constraints). (10 pts.)