Chapter 6.3, Problem 55E

In Problems 49-58, construct a mathematical model in the form of a linear programming problem. (the answers in the back of the book for these application problems indicate the model.) then solve the problem by applying the simplex method to the dual problem.

Human nutrition. A dietitian arranges a special diet using three foods: $L,M,$ and $N$. Each ounce of food $L$ contains $20$ units of calcium, $10$ units of iron, $10$ units of vitamin $\text{A}$, and $20$ units of cholesterol. Each ounce of food $M$ contains $10$ units of calcium, $10$ units of iron, $15$ units of vitamin $\text{A}$, and $24$ units of cholesterol. Each ounce of food $N$ contains $10$ units of calcium, $10$ units of iron, $10$ units of vitamin $\text{A}$, and $18$ units of cholesterol. If the minimum daily requirement are $300$ units of calcium, $200$ units of iron, and $240$ units of vitamin $\text{A}$, how many ounces of each food should be used to meet the minimum requirements and simultaneously minimize the cholesterol intake? What is the minimum cholesterol intake?