(FORTUNE Magazine) – The United States is swimming in milk, and the Department of Agriculture wants to mop it up. In a sweeping offensive against overproduction, the department will spend $1.8 billion to help nearly 14,000 farmers get out of the dairy business. The farmers must stay out of the business for five years, and they must dispose of their herds, marking each animal with a face brand that renders it illegal for dairy farming. More than 1.5 million cattle will be slaughtered or exported. Supplies of dairy products exceed demand by anywhere from 6% to 12% annually. The government supports prices by buying up excess production. Between fiscal 1979 and 1984, Washington spent some $9.9 billion to purchase and store unwanted dairy products. During much of that time, support prices fell -- from a high of $13.10 per hundred pounds of milk in 1981 to $11.60 in 1985 -- as Congress sought to control costs by legislating reductions. Yet last year's price-support programs still cost an estimated $2 billion. Will the latest program work? The Congressional Office of Technology Assessment projects that advances in animal feed and breeding will increase production per cow 43% by the turn of the century. Says an auditor at the General Accounting Office: ''The new program is a Band-Aid. In five years we'll be back to business as usual.''