Lisa Lives Out in the Country with Her Seven Cats

Lisa lives out in the country with her seven cats and avoids driving into the big city as much as possible. She has decided to make her own cat food and has the following nutritional guidelines. Each four ounce portion must contain 22 units of protein, 15 units of vitamin A, and 8 units of vitamin B. She has eggs, tomatoes, and chicken meat as possible inputs to her cat food. Each ounce of eggs contains 6 units of protein, 4 units of Vitamin A, and 3 units of Vitamin B. Each ounce of tomatoes contains 1 unit of protein, 8 units of Vitamin A, and 14 units of Vitamin B. Each ounce of chicken contains 22 units of protein, 14 units of Vitamin A, and 8 units of Vitamin B. Chicken costs 40 cents per ounce, tomatoes cost 5 cents per ounce, and eggs cost 12 cents per ounce. To make the production process as easy as possible, she would like to make exactly four ounces of cat food from her recipe. Formulate this decision as a linear programming problem, defining fully your decision variables and then giving the objective function and constraints.