A dietician wishes to ensure certain minimum intake of vitamins A,B and C for the patient. The minimum daily needs of vitamin A, B and C for the patient are 60, 40 and 32 units, respectively. For the supply of these vitamins the dietician relies on two fresh foods A and B. One kilogram of food A contains 14,10 and 4 units of vitamin A, B and C respectively. One kilogram of food B contains 4,8 and 16 units of the three vitamins, respectively. Food A costs £ 3 per kg and food B costs £2 per kg. How many kilograms of each food the dietician should buy every day to keep his food bill as low as possible and meet the minimum needs of the vitamin intake of his patient.
Questions
a) Formulate the problem as a linear programming model, clearly defining the variables, the objective function, and the constraints.
b) Solve the problem using Simplex method.
