A chicken farmer can buy a special food mix A at 20¢ per pound and a special food mix B at 40¢ per pound. Each pound of mix A contains 3,000 units of nutrient N₁ and 1,000 units of nutrient N₂; each pound of mix B contains 4,000 units of nutrient N₁ and 4,000 units of nutrient N₂. If the minimum daily requirements for the chickens collectively are 36,000 units of nutrient N₁ and 20,000 units of nutrient N₂, how many pounds of each food mix should be used each day to minimize daily food costs while meeting (or exceeding) the minimum daily nutrient requirements? What is the minimum daily cost? Construct a mathematical model and solve using the geometric method.