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.

1. Find and 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.

2. Imagine now that new measurements showed that the quantity of fat in meal 2 is 1 ounce and the quantity of fat in meal 3 is 3 ounces. Again solve the linear system and interpret the result.

3. Suppose now that in addition to the measurements in 2, the necessary amount of fat in the diet is changed to 9. Solve the linear system and interpret the result.