It is prescribed that the daily food ration for a patient m contain at least 100 units of vitamin A and 120 units of vitamin B. Two kinds of food, `F_1 and F_2`, are available for him. Food F, contains 6 units of vitamin A and 7 units of vitamin B per gram and costs 12 paise per gram; whereas food `F_2`, contains 8 units of vitamin A and 12 units of vitamin B per gram and costs 20 paise per gram. It is desired to determine a minimum cost diet for the patient. Formulate the problem as a linear programming problem and solve it graphically.