The Tetra Manufacturing Company has discontinued the production of a certain unprofitable product line. This act...

 

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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. 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.