Food and clothing are shipped to victims of a natural disaster. Each carton of food will feed 12 people, while each carton of clothing will help 5 people. Each 20-cubic-foot box of food weighs 50 pounds and each 5-cubic-foot box of clothing weighs 25 pounds. The commercial carriers transporting food and clothing are bound by the following constraints: - The total weight per carrier cannot exceed 24,000 pounds. - The total volume must be no more than 600 cubic feet. How many cartons of food and clothing should be sent with each plane shipment to maximize the number of people who can be helped?