Q1. A manufacturing firm has discontinued production of a certain unprofitable product line. This created considerable excess production capacity. Management is considering to devote this excess capacity to one or more of three product 1,2 and 3. The available capacity on the machines which might limit output are given below: Machine type Available time (in machine hours per week) Milling machine 250 Lathe 150 Grinder 50 The number of machine hours required for each units of the respective product is given below; Machine type Productivity (in machine hours/unit) Product 1 Product 2 Product 3 Milling 8 2 3 Lathe 4 3 0 Grinder 2 0 1 The unit profit would be 20 birr, 6 birr and 8 birr for products 1,2 and 3. Find how much of each product the firm should produce in order to maximise profit? Solve the problem by simplex method.​