Chapter 2.6, Problem 42E

DIET PLANNING Bob, a nutritionist who works for the University Medical Center, has been asked to prepare special diets for two patients, Susan and Tom. Bob has decided that Susan’s meals should contain at least $400\text{mg}$ of calcium, $20\text{mg}$ of iron, and $50\text{mg}$ of vitamin C, whereas Tom’s meals should contain at least $350\text{mg}$ of calcium, $15\text{mg}$ of iron, and $40\text{mg}$ of vitamin C. Bob has also decided that the meals are to be prepared from three basic foods: Food $A$, Food $B$ and Food $C$. The special nutritional contents of these foods are summarized in the accompanying table. Find how many ounces of each type of food should be used in a meal so that the minimum requirements of calcium, iron and vitamin C are met for each patient’s meals.

	Contents $\left(\text{mg}/\text{oz}\right)$
	Calcium	Iron	Vitamin C
Food $A$	30	1	2
Food $B$	25	1	5
Food $C$	20	2	4