Assume that the certain diet calls for seven units of fat, nine units of protein, and sixteen units of carbohydrates for main meal, and assume that individual has 3 possible foods to choose from to meet needs:
Food 1: Every ounce has 2 units of fat, two units of protein, and four units of carbohydrates.
Food 2: Every ounce has three units of fat, one unit of protein, and two units of carbohydrates.
Food 3: Every ounce has one unit of fat, three units of protein, and five units of carbohydrates
Consider x, y, and z denote number of ounces of first, second, and 3rd foods that dieter will consume at main meal. Determine (but do not solve) the linear system in x, y, and z whose solution tells how many ounces of every food must be consumed to meet diet needs.