A nutritionist, working for NASA, must meet certain minimum nutritional requirements and yet keep the weight of the food at a minimum. He is considering a combination of two foods, which are packaged in tubes. Each tube of food A contains 4 units of protein, 2 units of carbohydrates, and 2 units of fat and weighs pounds. Each tube of food B contains 3 units of protein, 6 units of carbohydrates, and 1 unit of fat and weighs pounds. The requirement calls for units of protein, units of carbohydrates, and units of fat. How many tubes of each food should be supplied to the astronauts?
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