Chapter 5.2, Problem 48E

Nutrition. A dietician in a hospital is to arrange a special diet using two foods. Each ounce of food $M$ contains $30$ units of calcium, $10$ units of iron, and $10$ units of vitamin A. Each ounce of food $N$ contains $10$ units of calcium, $10$ units of iron, and $30$ units of vitamin A. The minimum requirements in the diet are $360$ units of calcium, $160$ units of iron, and $240$ units of vitamin A. If $x$ is the number of ounces of food $M$ used and $y$ is the number of ounces of food $N$ used, write a system of linear inequalities that reflects the conditions indicated. Find the set of feasible solutions graphically for the amount of each kind of food that can be used.