Milky Way Dairy produces three products: Fresh Milk, Long-Life Milk, and Yogurt. Milky Way produces 50% of its raw milk needs and collects the reset from suppliers. Since these suppliers are required to bring the milk in their own cool tanks, they are paid $0.1 transportation cost per gallon. The raw milk produced in Milky Way’s farm as well as that collected from the suppliers is classified into three categories: Grade A, Grade B, and Grade C. The production process is accomplished over two separate stages. In the first stage, equal quantities of Grade A, Grade B, and Grade C milks are mixed and heated to produce Pre-Processed milk. If one gallon of each grade is mixed, they produce 3 gallons of Pre-Processed Milk. The heating cost for those 3 gallons is $1. In the second stage, the Pre-Processed milk is converted into the final products. Remaining quantities of the Pre-Processed milk can be sold for $3.25 / gallon. Fresh Milk is produced by heating Pre-Processed milk to 152 degrees Celsius. It cost $0.30 to convert one gallon of Pre-Processed milk into one gallon of Fresh Milk. Similarly, Long-Life milk is produced by heating Pre-Processed milk to 180 degrees Celsius. It costs $0.35 to convert one gallon of Pre-Processed milk into one gallon of Long-Life Milk. To produce the Yogurt, the company mixes one gallon of Pre-Processed milk with 14 units of Bacteria. The operation costs $0.40 and produces 28 units of Yogurt. The amounts of raw milk that Milky Way can obtain daily from its own farm and from suppliers, from Grade A, Grade B, and Grade C are 10,000, 11,000, 12,000 gallons respectively. The amount of Bacteria available daily is 25,000 units. Grade A costs $1.0 /gallon; Grade B costs $0.90 /gallon; and Grade C costs $0.80 /gallon. Each unit of Bacteria costs $0.03. Fresh Milk is sold for $3.75 /gallon; Long Life Milk is sold for $4.25 /gallon; and Yogurt is sold $0.40 /unit. Milky Way wants to maximize its profit from the daily production given that it can sell any quantities of its products, but only up to 1000 gallons of Pre-Processed milk. In addition, the company has recently signed a contract with a major supermarket chain to supply it daily with 5000 gallons of Fresh Milk and 1000 gallons of LongLife Milk.