The Tetra Manufacturing Company has discontinued the production of a certain unprofitable product line. This act created considerable excess production capacity. Management is considering devoting this excess capacity to one or more three products; call them products 1,2, and 3. The available capacity on the machines that might limit output is summarized in the table below: Available Time (Machine Hours per week) Machine Type Milling Machine 605 Lathe 325 Grinder 245 The number of machine hours required for each unit of the respective products is: Machine Type Milling Machine Lathe Product 1 Product 2 Product 3 1 6 0 2 Grinder 8 3 3 The sales department indicates that the sales potential for products 1 and 2 exceeds the maximum production rate and that the sales potential for product 3 is 15 units per week. The unit profit would be $45, $90 and $60, respectively. 1a) Define the decision variables for Tetra's product mix problem as accurately as possible. 1b) Write the objective function that maximizes Tetra's profit. 1c) Write all constraints of the model.