Chapter 5.3, Problem 60E

In Problems 49-64, construct a mathematical model in the form of a linear programming problem. (The answers in the back of the book for these application problems include the model.) Then solve by the geometric method.

Nutrition. A dietician is to arrange a special diet composed of two foods, $M$ and $N$. Each ounce of food $M$ contains $30$ units of calcium, $10$ units of iron, $10$ units of vitamin A, and $8$ units of cholesterol. Each ounce of food $N$ contains $10$ units of calcium, $10$ units of iron, $30$ units of vitamin A, and $4$ units of cholesterol. If the minimum daily requirements are $360$ units of calcium, $160$ units of iron, and $240$ units of vitamin A, how many ounces of each food should be used to meet the minimum requirements and at the same time minimize the cholesterol intake? What is the minimum cholesterol intake?