Suppose that a certain diet calls for 7 units of fat, 9 units of protein, and 16 units

Chapter 1, Problem 25

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Suppose that a certain diet calls for 7 units of fat, 9 units of protein, and 16 units of carbohydrates for the main meal, and suppose that an individual has three possible foods to choose from to meet these requirements: Food 1: Each ounce contains 2 units of fat, 2 units of protein, and 4 units of carbohydrates. Food 2: Each ounce contains 3 units of fat, 1 unit of protein, and 2 units of carbohydrates. Food 3: Each ounce contains 1 unit of fat, 3 units of protein, and 5 units of carbohydrates. Let x, y, and z denote the number of ounces of the first, second, and third foods that the dieter will consume at the main meal. Find (but do not solve) a linear system in x, y, and z whose solution tells how many ounces of each food must be consumed to meet the diet requirements.