3) A chemical manufacturing firm has discontinued production of a certain unprofitable product line. This has created considerable excess production capacity on the three exist- ing batch production facilities. Management is considering devoting this excess capacity to one or more of three new products: Call them products 1, 2, and 3. The available capac- ity on the existing units that might limit output is summarized in the following table: Unit Available time (l/week) A B 20 10 5 Each of the three new products requires the following processing time for completion: Productivity (h/batch) Unit Product 1 Product 2 Product 3 0.8 0.2 0.3 B 0.2 0.1 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 20 batches per week. The profit per batch is $20, $6, and $8, respectively, on products 1, 2, and 3. Formulate a linear programming model for determining how much of each prod- uct the firm should produce to maximize profit. 0.4 0,3