A farm is engaged in breeding hens. The hens are fed products A and B grown in the farm which contains nutrients P, Q and R. One kilogram of product A contains 36 units, 3 units and 20 units of nutrients P Q and R respectively, whereas one kilogram of product B contains 6 units, 12 units and 10 units of nutrients P, Q and R respectively. The minimum requirement of nutrients P Q and R for a hen is 108, 36 and 100 units respectively. Product A costs 20 per kilogram and product B costs 40 per kilogram. Using linear programming, find the number of kilograms of products A and B to be produced to minimize the total cost. Identify the feasible region from the rough sketch.