Feeding production livestock requires having a certain blend of nutrition for maximum health. In order to assure the health of dairy cattle, the daily feed should contain at least 22 grams (g) of fat, at least 32 g of carbohydrates, and at least 5 g of protein. Further, for good milk production, the diet should have at most 4 g of sodium and at most 5 g of potassium. Dairy farmers have access to three types of food, whose nutritional values (from the label on the package) are given in Table 1. Table 1 Nutritional values of livestock food Feed, oz Fat, g Carbohydrates, g Protein, g | Sodium, g Potassium, g Cost, $/oz Type 1 10 15 3 2 2 0.25 Type 2 12 12 3 1 2 0.30 Type 3 14 16 3 0.20 Formulate a linear programming problem for the optimal mix of food that will satisfy the nutritional requirements of the livestock and minimize the cost of feeding. Note that integer constraints should not be enforced on this problem, as there could be fractional amounts of feed types necessary to meet nutritional constraints