Janet Johnson has been watching the Dr. Iz show and concludes that her family needs at least 50 grams of protein and 15 milligrams of iron per day to maintain good health. Since Janet has recently converted to a vegan diet, she wants to make sure that the family gets all these nutrients solely from lentils and spinach. Each cup of lentils costs an average of $0.15 and contains 18 grams of protein and 5.5 milligrams of iron. Each cup of spinach costs $0.50 and has 1.1 grams of protein and 1.3 milligrams of iron.
Write the linear programming formulation to help Janet determine the quantities of lentils and spinach to meet the nutritional requirements at least cost.